Solve 2 log₇ 5 + log₇ x = log₇ 100.

Solution:

Given 2 log₇ 5 + log₇ x = log₇ 100.

We know that alogx = log xᵃ

log₇ 5² + log₇ x = log₇ 100.

We know that log a + log b with same base can be written as log (ab)

log₇ (25 * x) = log₇ 100

Applying anti-log on both sides

25x = 100

x = 4

Solve 2 log₇ 5 + log₇ x = log₇ 100.

Summary:

The value of x is 4 when 2 log₇ 5 + log₇ x = log₇ 100.