Solving Logarithmic Equations Questions 12







In this page solving logarithmic equations questions 12 we are going to see solution of twelfth problem from the worksheet. After understand the steps you can try other question listed below.

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.

Question 13

Find the value of x 

logx  + log x + log₈ x = 11/6

Solution:  

    logₓ 2  + logₓ 4 + logₓ 8 = 11/6

    1/logₓ 2  + 1/logₓ 2² + 1/logₓ 2³ = 11/6

    1/logₓ 2  + 1/2(logₓ 2) + 1/3(logₓ 2) = 11/6

    1/logₓ 2[1/1  + 1/2 + 1/3] = 11/6

    1/logₓ 2[(6 + 3 + 2 )/6] = 11/6

    log₂ x[11/6] = 11/6

    log = (11/6) x (6/11)

    log = 1

          = 2¹

          = 2


Question 1

Simplify log ₃ 15 - log ₃ 5 + 2 log ₃ 5


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 

logx x log16 = log256


Solution

Question 5

Find the value of x 

log(x + 2) + log₄ 3 = 2


Solution

Question 6

Find the value of x 

log(2x + 1) - log₃ (2x-1) = log₃ 4


Solution

solving logarithmic equations questions 12 solving logarithmic equations questions 12

Question 7

Find the value of x 

log10x - log₃ (x+1) = 2


Solution

Question 8

Find the value of x 

log(7x+3) - log₂ (5x-1) = log ₂ 3 - 1


Solution

Question 9

Find the value of x 

log(10+x) = log (3 + 4x)


Solution

Question 10

Find the value of x 

log(5 logx) = 2


Solution

Question 11

Find the value of x 

log√(10x + 5) - 1/2 = log√(x + 1)


Solution

Question 13

Find the value of x 

logx  + log 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 log3 x logx +1 = log₅ 3


Solution


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