Question

The function given is

y = 5^(log x)

We need the inverse, meaning we must rewrite it so that x is expressed in terms of y.

Step 1: Take log on both sides

log y = log(5^(log x))

Using the log rule

log(a^b) = b log a

So

log y = (log x)(log 5)

Step 2: Solve for log x

log x = (log y) / (log 5)

Step 3: Convert back from log form

If

log x = k

then

x = 10^k

x = 10^(log y / log 5)

Now use the identity

10^(log a / log b) = a^(1 / log b)

x = y^(1 / log 5)

x = y^(1 / log 5)

Therefore the inverse function is

That matches Option 3.

Original function raises 5 to a logarithmic power. When inverted, the variable moves into the base with a fractional exponent, which is why y gets raised to 1 / log 5.