Solve for x log base 4 of x=4

Problem

(log_4)(x)=4

Solution

1. Identify the logarithmic equation in the form (log_b)(x)=y where the base b=4 the argument is x and the exponent y=4

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

3. Substitute the values into the exponential form to get x=4

4. Evaluate the power by multiplying 4 by itself four times: 4×4×4×4=256

Final Answer

(log_4)(x)=4⇒x=256

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