Evaluate log base 64 of 4

Problem

(log_64)(4)

Solution

1. Identify the logarithmic equation by setting the expression equal to x

(log_64)(4)=x

2. Rewrite the equation in exponential form using the definition (log_b)(y)=x⇔bx=y

64=4

3. Express both sides of the equation using a common base, which is 4 in this case.

(4)x=4

4. Apply the power of a power rule (am)n=a(m*n) to the left side.

4(3*x)=4

5. Equate the exponents since the bases are now identical.

3*x=1

6. Solve for x by dividing both sides by 3

x=1/3

Final Answer

(log_64)(4)=1/3

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