Questions: Solve the following logarithmic equation. Be sure to reject any value logarithmic expression. Give the exact answer. log6 x=2 Rewrite the given equation without logarithms. Do not solve for x x=6^2

Solution Steps

1. Recognize that the given equation is a logarithmic equation.
2. Rewrite the logarithmic equation in its exponential form.
3. Solve for \( x \) by calculating the exponentiation.

The given logarithmic equation is

\[ \log_{6}(x) = 2 \]

To rewrite this equation in exponential form, we use the definition of logarithms, which states that if

\[ \log_{b}(a) = c \]

then

\[ a = b^{c} \]

Applying this to our equation, we have:

\[ x = 6^{2} \]

Now, we compute \( 6^{2} \):

\[ x = 36 \]

Final Answer