What is the solution of log_{2x - 5} 25 = 2?

Solution:

Given function is log_{2x - 5} 25 = 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 b^y = x.

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

⇒ log_{2x - 5} 25 = 2

(2x - 5)² = 25

(2x - 5) = ± 5

Consider, (2x - 5) = 5

2x = 5 + 5

2x = 10

x = 5

Note: -5 cannot be considered as the base of the logarithm cannot be negative.

What is the solution of log_{2x - 5} 25 = 2?

Summary:

The solution of log_{2x - 5} 25 = 2 is 5.