Solve for x log base 4 of x=2

Problem

(log_4)(x)=2

Solution

1. Identify the logarithmic equation in the form (log_b)(y)=a where the base b=4 the argument y=x and the exponent a=2

2. Rewrite the equation in its equivalent exponential form using the definition (log_b)(y)=a⇔ba=y

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

4. Evaluate the power by calculating 4×4

Final Answer

(log_4)(x)=2⇒x=16

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