Question

Find the value of x:

log_x 8 = 2 – log_x 18

Answer 1

We are given the equation:

log_x 8 = 2 – log_x 18

Step 1: Move the terms involving logarithms to one side

Rearrange the equation:

log_x 8 + log_x 18 = 2

Step 2: Use the logarithmic property

Use the property log_b a + log_b c = log_b(ac):

log_x(8 × 18) = 2

Simplify the product inside the logarithm:

log_x 144 = 2

Step 3: Convert to exponential form

The equation log_x 144 = 2 can be written in exponential form:

x² = 144

Step 4: Solve for x

`x = +-sqrt(144) = +-12`

Since the base of the logarithm x must be positive, we discard the negative solution.

Thus, the value of x is: x = 12