Evaluate log base 4 of 64

Problem

(log_4)(64)

Solution

1. Identify the logarithmic expression as an equation where 4 raised to some power x equals 64

(log_4)(64)=x

2. Rewrite the equation in exponential form using the definition of a logarithm.

4=64

3. Express the number 64 as a power of the base 4

64=4⋅4⋅4

64=4

4. Substitute the power back into the exponential equation.

4=4

5. Solve for x by equating the exponents since the bases are the same.

x=3

Final Answer

(log_4)(64)=3

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