Solve for x log base 6 of x=3

Problem

(log_6)(x)=3

Solution

1. Identify the logarithmic equation in the form (log_b)(x)=y where the base b=6 the argument is x and the exponent y=3

2. Rewrite the equation in its equivalent exponential form using the definition of a logarithm, which states that (log_b)(x)=y⇔by=x

3. Substitute the known values into the exponential form to get x=6

4. Calculate the value of the base raised to the power by multiplying 6×6×6

5. Simplify the result to find the value of x

Final Answer

(log_6)(x)=3⇒x=216

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