Solving Logarithmic Equations Worksheet







In this page solving logarithmic equations worksheet we are going to see some practice questions. You can find solution for each problem. You can try each problems on your own. If you find it difficult to do any problems please click solution to know how the problem has been solved. Now you are going to see basic points to workout any problems easily.

For solving any critical questions in this topic we have to remember the following points listed below.

Points to remember:

  • Consider whether the given logarithmic terms are having same base. If they don’t have same base we have to make them with same base.
  • If  there is any number before log we have to write them as power using power formula
  • Combine them using logarithmic formulas
  • If two log terms is being both sides of equal symbol we can equalize the number without log.

Let us see different type of problems to understand this topic better.

Questions

Solutions

Question 1

Find the value of x 

2 log ₅ x  = 3 log ₅ 2


Solution

Question 2

Find the value of x 

log ₃ x + log ₃ 7 = log ₃ 11


Solution

Question 3

Find the value of x 

x log ₁₆ 8 + 1 = 0


Solution

Question 4

Find the value of x 

log₄ x x log₄ 16 = log₄ 256


Solution

Question 5

Find the value of x 

log₄ (x + 2) + log₄ 3 = 2


Solution

Question 6

Find the value of x 

log₃ (2x + 1) - log₃ (2x-1) = log₃ 4


Solution

Question 7

Find the value of x 

log₃ 10x - log₃ (x+1) = 2


Solution

Question 8

Find the value of x 

log₂ (7x+3) - log₂ (5x-1) = log ₂ 3 - 1


Solution

Question 9

Find the value of x 

log₅ (10+x) = log ₅ (3 + 4x)


Solution

Question 10

Find the value of x 

log₅ (5 log₃ x) = 2


Solution

Question 11

Find the value of x 

log₃ √(10x + 5) - 1/2 = log₃ √(x + 1)


Solution

Question 12

Find the value of x 

log₂ x  + log ₄ x + log₈ x = 11/6


Solution

Question 13

Find the value of x 

log₃ x  + log₉ x + log₈₁ x = 7/4


Solution

Question 14

Find the value of x 

log (x + 1) + log (x - 1) = log 24


Solution

Question 15

Find the value of x 

2 log₅ 3 x log₉ x +1 = log₅ 3


Solution

Solving Logarithmic Equations Worksheet