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Form 2 Questions and Answers on Indices and Logarithms

Form 2 Questions and Answers on Indices and logarithms. In this course, we are going to learn through worked out examples. Answers are in video format.

Lessons (99)

• 1.    Solve for x in: #9^x+3^(2x)-1=53#
  3m 11s

• 2.    Solve the equation : #9^(x+1)+3^(2(x+1))=36#
  4m 35s

• 3.    Find the value of x in the following equation: #49^(x+1)+7^(2x)=350#
  3m 40s

• 4.    Given that #9^(2y) ×2^x=72#, Find the value of x and y
  4m 13s

• 5.    Two numbers p and q are such that #p^3×q=189#. Find p and q
  1m 38s

• 6.    Given that #9^(4/3)=3^n#,find the value of n
  1m 52s

• 7.    Find the value of x which satisfies the equation: #16^(x^2)=8^(4x-3)#
  7m 20s

• 8.    Find the value of m in the following equation: #(1/27)^m×(81)^-1=243#
  4m 39s

• 9.    Solve for x in the equation: #(81^(2x)×27^x)-:9^x=729#
  3m 32s

• 10.    Without using a calculator or mathematical tables, evaluate #(27)^(2/3)×(81/16)^(-1/4)#
  4m 17s

• 11.    Simplify #(27^(2/3)-:2^4)-:32^(-3/5)#
  2m 59s

• 12.    Without using logarithm tables or calculators, evaluate, #(64^(-1/2)×27000^(2/3))-:(2^-4×3^0×5^2)#
  7m 1s

• 13.    Solve for x: #4^(x+1)=32#
  1m 44s

• 14.    Solve for x in the equation: #32^((x-3))× 8^((x+4))=64-:2^x#
  4m 52s

• 15.    Simplify: #(2^x×5^(2x)÷2^(-x))^(1/2)#
  2m 54s

• 16.    Find the value of y in the equation: #(243×3^(2y))/ (729×3^y-:3^((2y-1))) = 81 #
  5m 48s

• 17.    Simplify: #(243^(-2/5)×125^(2/3)) /(9^(-3/2))#
  3m 12s

• 18.    Simplify: #(25^(3/4)×0.9^2×2^2)/(5^(5/2)×3^3)#
  3m 13s

• 19.    Given that #6^(2(n-3))=7776#, find the value of n.
  4m 17s

• 20.    Given that P=3y express the equation #3^(2y-1)+2×3^(y-1)=1# in terms of P. Hence or otherwise find the value of y in the equation #3^(2y-1)+2×3^(y-1)=1#
  5m 58s

• 21.    Use logarithms to evaluate: #root(3)((35.6 times 0.0613^2))#
  9m 59s

• 22.    Evaluate: #frac{1.34}{(5.24^0.8)times 0.0029}#
  7m 58s

• 23.    Use mathematical tables to evaluate: #sqrt(( frac{2.935times0.0765}{32.74}))#
  11m 24s

• 24.    Use logarithms to evaluate: #root(3)((frac{7.08}{76.8times7.034}))#
  9m 4s

• 25.    Use mathematical tables to evaluate: #frac{sqrt 0.0645}{0.0082}#
  5m 20s

• 26.    Use logarithms to evaluate #root(4)(frac{4.562 times0.038}{0.82})#
  8m 52s

• 27.    Use logarithms to evaluate #frac{(0.07284)^2}{root(3)(0.06195)}#
  9m 34s

• 28.    Use logarithms to evaluate #root(3)(frac{36.15times0.02573}{1.938})#
  10m 8s

• 29.    Use logarithms to evaluate: #frac{(1934)^2 times sqrt0.00324}{436}#
  12m 11s

• 30.    Use logarithms to evaluate: #55.9div (0.2621 times 0.01177)^(1/5)#
  11m 49s

• 31.    Use logarithms to evaluate #(frac{6.79times0.3911}{log 5})^(3/4)#
  9m 38s

• 32.    Use logarithms to evaluate #root(3)(frac{1.23times0.0089}{76.54})#
  8m 40s

• 33.    Use logarithms to evaluate: #(3.256 times 0.0536)^(1/3)#
  6m 57s

• 34.    Use logarithms to evaluate #frac{(0.0056)^(1/2)}{ 1.38 times 27.42}#
  8m 46s

• 35.    Use logarithm tables to evaluate #frac{2347times0.04666}{root(3)(0.0924)}#
  11m 3s

• 36.    Use logarithms to evaluate #frac{34.33}{sqrt(5.25times0.042)}#
  7m 43s

• 37.    In this question, show all the steps in your calculations, giving your answer at each stage. Use logarithms, correct to 4 decimal places, to evaluate: #root(3)(frac{36.72times(0.46)^2}{185.4})#
  9m 27s

• 38.    Use logarithm tables to evaluate: #(frac{0.032times14.26}{0.006})^(2/3)#
  6m 21s

• 39.    Use logarithms, correct to 4 decimal places, to evaluate: #root(3)(frac{83.46times0.0054}{1.56^2})#
  9m 28s

• 40.    Use logarithms, correct to 4 decimal places, to evaluate #root(3)(frac{1.794times0.038}{1.243})#
  8m 56s

• 41.    Find the numerical value of: (a) #9^(1/2)# (b) #25^(-1/2)# (c) #36^(3/2)# (d) #8^(-5/3)#
  2m 2s

• 42.    Find the numerical value of each of the following: (a) #(3^(-2))^3# (b) #(49^2)^(-1/2)# (c) #(10^3)^(5/3)#
  1m 7s

• 43.    Simplify each of the following expressions leaving your answer in index form. (a) #3^3×3^4# (b) #5^2×5^(-3)# (c) #3^(3/2)×3^(-3/4)×3^(1/4)# (d) #6^2×7^(-4)×(8^(-2))^2×6^3×7^2×8^4#
  3m 52s

• 44.    Simplify the following expressions leaving your answer in index form. (a) #512^(2/3)×8^(1/3)div2^6# (b) #(2^(-2)×(2^2)^(-6))/(2^(-4)×2^(-6) )# (c) #(6/7)^(-2)×(7/6)^(-2)#
  4m 38s

• 45.    Simplify the following: (a) #r^3×r^2 t^2×r^(-3) t^(-2)# (b) #(a^n×a^m)/(a^(-n)×a^(-m) )# (c) #(x^2 y^3×x^4 y^2)/(x^3 y^4 )# (d) #(a^4 b^3×a^2 c^4×b^(-2) c^3)/(a^(-3) b^3 c^3 )#
  5m 47s

• 46.    Simplify: (a) #(25y^9 k^(-7))/(81y^7 k^9 )# (b) #(3^(-4) a^4 b^6)/(3a^5 b^8 )# (c) #((a^(-n))^m×a^(-2m))/(a^mn×a^2m )#
  4m 28s

• 47.    Simplify the expressions: (a) #(9a^2)^(1/3)/6^4 ×(4b^2)^(1/3)/5a# (b) #root3((27x^3 y^9)/(x^6 y^3 ))# (c) #(root5(32y^10 k^15 2^10 ) )/root4((16y^12 k^16 2^4 ) )#
  8m 37s

• 48.    Solve each of the following equations: (a) #(3^2x)^3=3^4×3^8# (b) #(7^5)^x=(7^4)^xdiv7^2# (c) #(64^2ydiv16^y)/(128^y×4^2y )#
  4m 24s

• 49.    Find the logarithms to base of 10 of: (a) 0.149 (b) 0.0000784 (c) 8.2 (d) 475000
  2m 34s

• 50.    Find the antilogarithms of the following numbers. (a) #bar1#. 1080 (b) #bar4#. 8938
  2m 14s

• 51.    Calculate: (a) #bar2# . 34 + #bar4# . 30 (b) #bar3# . 79 - #bar2# . 24
  1m 11s

• 52.    Use logarithms and antilogarithm tables to evaluate: (a) 251 × 367 (b) 7.32 × 199
  5m 51s

• 53.    Use logarithms and antilogarithm tables to solve: (a) 1500 ÷ 750 (b) 43.1 ÷ 3.17
  4m 37s

• 54.    Use logarithms and antilogarithm tables to evaluate the following: (a) #(291 ×681)/372# (b) #(1024 ×6561)/(4096 ×729)#
  9m 14s

• 55.    Use logarithm table to find (i) the square root and (ii) the cube root of: (a) 478 (b) 0.0067
  6m 48s

• 56.    Use tables to evaluate: (a) #sqrt((3.142 ×2.718)/(6.49 ×81.2))# (b) #(41.56 ×52.3)/sqrt42.88#
  9m 1s

• 57.    Find the numerical value of: (a) #36^(-1/2)# (b) #35769^0# (c) #81^(1/2)# (d) #27^(-1/3)# (e) #16^(5/2)# (f) #100^(9/2) # (g) #64^(4/3)# (h) #256^(3/4)# (i) #729^(1/3)# (j) #(216^2 )^(1/3)# (k) #243^(2/3)# (l) #4096^(-3/4)# (m) #64^(-1/(6 ))#
  5m 58s

• 58.    Simplify each of the following expressions. You may leave your answer in index form: (a)# 2^3×2^5×2^(-4) # (b)# 20^(-3)×25^2×20^3×25^(-4)# (c)#7^(-3)×8^4×7^2×8^(-3)# (d)#27^(1/3)×9^(1/2)# (e)#(3/4)^2×(3/4)^3# (f) #(20^(-2)×20^(-2)×20^(-2))/20# (g)# 2^(-6)×5^(1/2)×2^7÷2^(-4)#
  4m 48s

• 59.    Simplify: #(a) x^2×x^4# #(b) y^3×y^6# #(c) n^13×n^(-7)# #(d) a^9×a^3# #(e) a^(-2)×3a^4# #(f)(2n)^3×(2n)^5# #(g) x^16÷n^12# #(h) a^15÷a^14# #(i) a^2×b^2×a^4#
  2m 35s

• 60.    Simplify: (a)# b^2×x^2×b^11# (b)# b^3×n^2×b^0×n^3# (c)# a^5×c^2×a^3×b^3×a^4# (d)# a^(-2)×b^2×a^(-8)×b^(-4)# (e)# x^2 y^2× x^2 y^5× x^(-3) y^(-9)# (f)#(xyt)^n÷(xyt)^2# (g) #(a^x×a^2x)/(a^x×a^x×a^x )#
  3m 13s

• 61.    Simplify: (a)#(12a^5 b^3)/(4a^3 b)# (b)#(a^(-a)×b^(-a)×c^(-a))/(a^(-2a)×b^(-2a)×c^(-2a) )# (c)#(rs^2 t^3×r^4 s^5 t^(-6)×r^7 s^8 t^(-9))/(r^10 s^11 t^(-12)×r^13 s^(-14) t^15 )# (d)#((16a^2 )^(1/2)×(36a^4 )^(-1/2))/(2a^(1/2)×5a^(3/2)×8a^(9/4) )#
  6m 53s

• 62.    Solve each of the following equations: (a) #(3^(2x) )^4=81# (b) #4^(5x)÷(2^(3x ))^2=256# (c) #9^(2x)=729# (d) #2^(8x)=512# (e) #(7^4 )^(2x)=(7^4 )^3# (f) #(5^3 )^a×(5^8 )^a= 5^72#
  3m 54s

• 63.    Solve each of the following equations: (a) #9^(4x)÷3^(2x)=2187# (b) #(5^(2c) )^3=(5^4 )^c×625# (c)# 2^(x/4)=8# (d)# 3^((2x-5))=27# (e)# 3^(4x)÷3^(-7)=3^15# (f) #2×3^x=162#
  4m 40s

• 64.    Write in form of #a^n# where a=2 (i) 2 (ii) 4 (iii) 1 (iv)# 1/2# (v) #1/4#
  0m 47s

• 65.    Write in form of #a^n# where a=3 (i) 27 (ii) 9 (iii) 3 (iv) 1 (v) #1/3# (vi)# 1/9# (vii) #1/27#
  0m 53s

• 66.    Write in form of #a^n# where a=10 (i) 1000 (ii) 100 (iii) 10 (iv) 1 (v) #1/10# (vi)# 1/100# (vii) #1/1000#
  1m 5s

• 67.    Copy and complete the table below:
  1m 25s

• 68.    Write in logarithmic form: (a) #3^2 = 9# (b) #2^4 = 16# (c) #3^3 = 27# (d) #2^5 = 32 # (e) #3^4 = 81# (f) #5^3=125# (g) #10^0= 1# (h) #2^10 = 1024 # (i) #a^n=b#
  1m 25s

• 69.    Write each of the following in index form: (a) #log_2 8 = 3# (b) #log_4 16 = 2# (c) #log_5 125 = 3# (d) #log_10 8 = x# (e) #log_b a = c# (f) #log_3 27 = 3# (g) #log_6 216= 3# (h) #log_x 40 = y# (i) #log_y x = 2# (j) #log_10 10000 = 4# (k) #log_4 6 = y# (l) #log_2 16 = 4#
  1m 33s

• 70.    Use logarithm table to express each of the following numbers in the form #10^x#. (a) 681.4 (b) 1.47 (c) 4.73 (d) 7.25 (e) 9.83 (f) 5.672 (g) 8.137 (h) 3.142 (i) 2.718
  6m 45s

• 71.    Use logarithm table to express each of the following numbers in the form #10^x#. (a) 3.333 (b) 12.3 (c) 59.7 (d) 82.9 (e) 72 (f) 96.1 (g) 431.5 (h) 7924 (i) 1025
  6m 47s

• 72.    Use logarithm table to express each of the following numbers in the form #10^x#. (a) 1913 (b) 4937 (c) 273.7 (d) 3,910,000 (e) 958,312
  3m 54s

• 73.    Find the logarithms to base 10 of: (a) 0.2843 (b) 0.3520 (c) 0.4286 (d) 0.0694 (e) 0.0485 (f) 0.0239 (g) 0.000376 (h) 0.0000523
  3m 57s

• 74.    Find the antilogarithms of the following numbers: (a) #bar1 .2480# (b) #bar2 .3927# (c) #bar2 .5403# (d) #bar3 .6503#
  3m 27s

• 75.    Find the antilogarithms of the following numbers: (a) #bar3 .9750# (b) #bar2 .5658# (c) #bar5 .4533# (d) #bar3 .6821#
  3m 5s

• 76.    Calculate: (a) #bar2 .37+1.20# (b) #bar5 .63+bar2 .57# (c) #bar7 .12-bar5 .54# (d) 5.27 -#bar2 .73#
  3m 11s

• 77.    Use logarithm and antilogarithm tables to evaluate: (a) #4192times3078# (b) #21.47times362.1#
  5m 30s

• 78.    Use logarithm and antilogarithm tables to evaluate: (a) #26.1times91.2times45.7# (b) #33.2times172times44.32#
  7m 25s

• 79.    Use logarithm and antilogarithm tables to evaluate: (a) #1527times3196times4157# (b) #7.312times49.45times157.2#
  8m 49s

• 80.    Use logarithm and antilogarithm tables to evaluate: (a) #16.31×152.1×3290# (b) #100×245×175×396#
  7m 28s

• 81.    Use logarithm and antilogarithm tables to evaluate: (a) #2145div560# (b) #412div241# (c) #882div144# (d) #3612div452#
  9m 19s

• 82.    Use logarithm and antilogarithm tables to evaluate: (a) #1111div222# (b) #3.142div2.718# (c) #9250div4312# (d) #6380div2137#
  10m 1s

• 83.    Use logarithm and antilogarithm tables to evaluate: (a) #(634×436×688)/784# (b) #(3041×3211)/2112#
  8m 6s

• 84.    Use logarithm and antilogarithm tables to evaluate: (a) #(788×576)/675# (b) #(294+578)/(368-275)#
  6m 58s

• 85.    Use logarithm and antilogarithm tables to evaluate: (a) #(839+672)/(762+393)# (b) #(3267-37)/(2236+89)#
  6m 36s

• 86.    Use logarithm and antilogarithm tables to evaluate: (a) #(29^2×33^3)/64^4 # (b) #(18^2×391^4)/(15^3×56^4 )#
  9m 38s

• 87.    Use logarithm and antilogarithm tables to evaluate: (a) #876.9/(61.2times3.85)# (b) #518.3/(29.5times714)# (c) #(48.35times125.3)/(39.3times50.4)#
  11m 4s

• 88.    Use logarithm and antilogarithm tables to evaluate: (a) #(3.74times7.82)/5.4# (b) #399.6/(15.2times4.83times1.98)# (c) #734.4/(25.1times6.34times3.4)#
  9m 45s

• 89.    Use logarithm and antilogarithm tables to evaluate: (a) #(94.7times16.45)/(12.5times8.93)# (b) #(4.48)^3/(3.16)^2 # (c) #(171.5)^3/(56.3times26.98)# (d) #(79.36)^3/(8.2times(9.2)^2 #
  17m 4s

• 90.    Use logarithms to evaluate: (a) #0.9063times3.387# (b) #0.5060times0.05707# (c) #36.65times0.4163times0.007022# (d) #26.68div255.4#
  12m 51s

• 91.    Use logarithms to evaluate: (a) #3.404div628# (b) #(0.0075times0.8181)/0.00509# (c) #77.9/(0.988times9100)#
  11m 41s

• 92.    Use logarithms to evaluate: (a) #(2.89times5.27)/(62.25times1.908)# (b) #(34.53times361.6)/(343.7times615.8)# (c) #(91.3div18.26)/(75.4div12.09)#
  14m 57s

• 93.    Divide each of the following logarithms by 2. (a) 0.8938 (b) 1.8624 (c) #bar2 .9754# (d) #bar1 .7076# (e) #bar1 .8538 # (f) #bar2 .3502# (g) #bar2 .1644# (h) #bar3 .4928# (i) #bar3 .6946# (j) #bar4 .7938#
  6m 5s

• 94.    Divide each of the following logarithms by 3. (a) 0.8938 (b) 1.8624 (c) #bar2 .9754# (d) #bar1 .7076# (e) #bar1 .8538 # (f) #bar2 .3502# (g) #bar2 .1644# (h) #bar3 .4928# (i) #bar3 .6946# (j) #bar4 .7938#
  8m 49s

• 95.    Divide each of the following logarithms by 4. (a) 0.8938 (b) 1.8624 (c) #bar2 .9754# (d) #bar1 .7076# (e) #bar1 .8538 # (f) #bar2 .3502# (g) #bar2 .1644# (h) #bar3 .4928# (i) #bar3 .6946# (j) #bar4 .7938#
  9m 4s

• 96.    Use logarithm table to find (i) the square root and (ii) the cube root of: (a) 2461 (b) 3572 (c) 4683 (d) 0.0346
  12m 39s

• 97.    Use logarithm table to find (i) the square root and (ii) the cube root of: (a) 0.00457 (b) 0.00072 (c) 78.039 (d) 361.472
  13m 20s

• 98.    Use tables to evaluate: (a) #root2(((3.45×16.7)/31.5) )# (b) #root3(((1.794×0.038)/12.43) )# (c) #root3(((39.51×725)/0.758) )#
  11m 48s

• 99.    Use tables to evaluate: (a) #root3(((4862×725)/(6437×1024)) )# (b) #root4(((6978×25.1)/132.7) )#
  12m 8s