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 1Simplify log ₃ 15 - log ₃ 5 + 2 log ₃ 5 Solution Question 2Find the value of x  log ₃ x + log ₃ 7 = log ₃ 11 Solution Question 3Find the value of x  x log ₁₆ 8 + 1 = 0 Solution Question 4Find the value of x  log₄ x x log₄ 16 = log₄ 256 Solution Question 5Find the value of x  log₄ (x + 2) + log₄ 3 = 2 Solution Question 6Find the value of x  log₃ (2x + 1) - log₃ (2x-1) = log₃ 4 Solution solving logarithmic equations questions 12 solving logarithmic equations questions 12 Question 7Find the value of x  log₃ 10x - log₃ (x+1) = 2 Solution Question 8Find the value of x  log₂ (7x+3) - log₂ (5x-1) = log ₂ 3 - 1 Solution Question 9Find the value of x  log₅ (10+x) = log ₅ (3 + 4x) Solution Question 10Find the value of x  log₅ (5 log₃ x) = 2 Solution Question 11Find the value of x  log₃ √(10x + 5) - 1/2 = log₃ √(x + 1) Solution Question 13Find the value of x  log₃ x  + log₉ x + log₈₁ x = 7/4 Solution Question 14Find the value of x  log (x + 1) + log (x - 1) = log 24 Solution Question 15Find the value of x  2 log₅ 3 x log₉ x +1 = log₅ 3 Solution