Logarithmic Equations and Examples with Solutions for SSC and Bank Exams

Logarithm quantitative aptitude questions asked in competitive exams often. Most of the students face difficulties while solving logarithmic problems because they don't practice logarithmic problems with solutions.

Here in this blog, you can simply resolve your difficulties of logarithmic problems with solutions. So try to solve logarithm problems own self easily and learn how to solve logarithm problems with solutions.

After learning you can more practice with logarithm questions with answers for ssc and bank exams and can improve your performance level also.

Logarithmic Problems with Solutions for Competitive Exams:

Logarithm equation examples and problems with solution 

Q.1. The value of log₃₄₃ 7 is :

$$(a) \ {1\over3} \ (b) \ -3\ (c) \  -{1\over3}\ (d) \ 3 $$

Solution

Let log₃₄₃ 7 = n. Then, (343)ⁿ = 7 ↔ (7³)ⁿ = 7 ↔ 3n= 1

$$  ↔n={1\over3}.$$ $$∴ log_{343}7={1\over3}$$

Q.2. The value of log_√232 is : 

$$(a) \ {5\over2} \ (b) \ 5\ (c) \  10\ (d) \ {1\over10} $$

Solution

Let log√₂32=n. Then, (√2)ⁿ=32↔(2)^n/2=2⁵

$$  ↔{n\over2}=5↔n=10.$$ $$∴ log_\sqrt{2}32=10.$$

Q.3. The value of log_(.01)(1000) is :

$$(a) \ {1\over3} \ (b) \ -{1\over3}\ (c) \  {3\over2}\ (d) \ -{3\over2}\  $$

Solution

Let log_(.01) (1000) = n.

Then, (.01)ⁿ = 1000

$$↔ \left({1\over100}\right)^n=10^3$$

↔ (10^-2n) = 10³↔ - 2n=3 $$↔ n=-{3\over2}$$

Q.4. if log₃x = - 2, then x is equal to :

$$(a) \ -9 \ (b)-6 \   (c) \ -8 \ (d) \ {1\over9}\  $$

Solution

Log₃x = -2 ↔ x = 3^-2$$={1\over3^2}={1\over9}$$

Q.5. If log_x =  , then x is equal to : 

$$(a) \ -{3\over4} \ (b)\ {3\over4} \  (c) \ {81\over256} \ (d) \ {256\over81}\  $$

Solution

   $$log_x=\left({9\over16}\right)=-{1\over2}⟺x^{-1/2}={9\over16}$$

  $${1\over \ \sqrt x\ }={9\over16}⟺ \sqrt x\ = {16\over9}$$

$$x=\left({16\over9}\right)^2={256\over81}$$

Q.6. The value of log₂ 16 is :

$$(a) \ {1\over8} \ (b) \ 4\ (c) \ 8\ (d) \ 16 $$

Solution

Let log₂ 16 = n. Then, 2ⁿ = 16 = 2⁴→n=4.

∴ log₂ 16 = n.

Q.7. The value of log₅  is :

$$(a) \ 3 \ (b) \ -3\ (c) \  {1\over3}\ (d) \ -{1\over3} $$

Solution

$$ Let \ log_5\left({1\over125}\right)=n.$$

   $$Then, 5^n={1\over125}↔ 5^n= 5^{-3}↔n=-3$$

   $$∴ log_5\left({1\over125}\right)=-3.$$

Q.8. The value of log₁₀(.0001) is :

$$(a) \ {1\over4} \ (b) \ -{1\over4}\ (c) \  -4\ (d) \ 4 $$

Solution

Let log₁₀(.0001)=n.

Then, 10ⁿ = 0.001

$$ ↔10^n={1\over1000}={1\over10^4}$$

↔ 10n=10^–4 ↔ n = -4.

∴ log₁₀ (.0001) =-4

Q.9. The logarithm of 0.0625 to the base 2 is :

$$(a) \ -4 \ (b)-2 \  (c) \ 0.25   \ (d) \ .5\  $$

Solution

Let log₂0.0625 = n. Then 2n = 0.0625

$$={625\over10000}↔2^n={1\over16}↔2^n=2^{-4}↔n=-4.$$

∴ log₂ 0.0625= - 4 

Q10. If log₈ x= , then the value of x is :

$$(a) \ {3\over4} \ (b)\ {4\over3} \  (c) \ 3 \ (d) \ 4\  $$

Solution

$$log_8x={2\over3}↔x=8^{2/3}=(2^3)^{2/3}$$

==2²=4

I hope these solutions are helpful for your preparation. If you have any problems or doubt regarding logarithmic equations examples and problems with solutions or you want ask any questions, you can ask me in the comment section. 

All the best for your exam