Solve for x log base 6 of 36=x

Problem

(log_6)(36)=x

Solution

1. Identify the logarithmic equation, which is in the form (log_b)(y)=x

2. Rewrite the equation in its equivalent exponential form using the definition of a logarithm, bx=y

(log_6)(36)=x⇒6=36

3. Express the number 36 as a power with a base of 6 to make the bases on both sides of the equation match.

36=6

4. Substitute the power back into the exponential equation.

6=6

5. Equate the exponents since the bases are equal.

x=2

Final Answer

(log_6)(36)=2

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