Question

Find the value of x:

log₅ (x² + 9) = 2

Answer 1

log₅ (x² + 9) = 2

Step 1: Convert to exponential form:

The logarithmic equation log_b a = c is equivalent to b^c = a.

So, applying this to the given equation:

5² = x² + 9

Step 2: Simplify the equation:

Since 5² = 25, we have:

25 = x² + 9

Step 3: Solve for x:

x² = 25 – 9

x² = 16

`x = +-sqrt(16)`

x = ±4