Question

Find the value of x:

`log_sqrt(5) (log_3x) = 2`

Answer 1

`log_sqrt(5) (log_3x) = 2`

Step 1: Convert the logarithmic equation to exponential form:

The equation log_b a = c can be written as b^c = a.

Applying this to the given equation:

`sqrt(5)^2 = log_3x`

Since `sqrt(5)^2 = 5`, we get:

5 = log₃ x

Step 2: Convert to exponential form:

Now, log₃ x = 5 implies:

x = 3⁵

Step 3: Calculate x.

x = 3⁵ = 243