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

log ₂ x + log ₄ x + log₈ x = 11/6

Solution :

log ₓ 2 + log ₓ 4 + log ₓ 8 = 11/6

1/log ₓ 2 + 1/logₓ 2 ²
+ 1/logₓ 2 ³ = 11/6

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

1/ log ₓ 2 [1/1 + 1/2 + 1/3] = 11/6

1/ log ₓ 2 [(6 + 3 + 2 )/6] = 11/6

log ₂ x [11/6] = 11/6

log ₂ x = (11/6) x (6/11)

log ₂ x = 1

x = 2 ¹

x = 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

log ₄ x x log ₄ 16 = log ₄ 256

Solution

Question 5

Find the value of x

log ₄ ( x + 2) + log₄ 3 = 2

Solution

Question 6

Find the value of x

log ₃ ( 2x + 1) - log ₃ (2x-1) = log ₃ 4

Solution

solving logarithmic equations questions 12 solving logarithmic equations questions 12

Question 7

Find the value of x

log ₃ 10 x - log ₃ (x+1) = 2

Solution

Question 8

Find the value of x

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

Solution

Question 9

Find the value of x

log ₅ (10+x) = log ₅ (3 + 4x)

Solution

Question 10

Find the value of x

log ₅ (5 l og ₃ x) = 2

Solution

Question 11

Find the value of x

log ₃ √(10x + 5) - 1/2 = l og ₃ √(x + 1)

Solution

Question 13

Find the value of x

log ₃ x + log ₉ x + log₈ ₁ 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 log ₅ 3 x lo g ₉ x +1 = log ₅ 3

Solution