What is the solution of log_{3x - 5} 16 = 2?

Solution:

Given function is log_{3x - 5} 16 = 2

By definition of the logarithmic function: If ‘b’ is any number such that b> 0 and b≠1 then y = log_bx is equivalent to by = x.

Here y = log_bx is called the logarithm form and b^y = x is called the exponential form.

⇒ log_{3x - 5} 16 = 2

(3x - 5)² = 16

(3x - 5) = ± 4

Consider, (3x - 5) = 4

3x = 4 + 5

3x = 9

x = 3

Note: -4 cannot be considered as a base of the logarithm cannot be negative.

What is the solution of log_{3x - 5} 16 = 2?

Summary:

The solution of log_{3x - 5} 16 = 2 is 3.