Evaluate log base 625 of 5

Problem

(log_625)(5)

Solution

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

(log_625)(5)=x

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

625=5

3. Express the base 625 as a power of 5 to create a common base.

(5)x=5

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

5(4*x)=5

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

4*x=1

6. Solve for x by dividing both sides by 4

x=1/4

Final Answer

(log_625)(5)=1/4

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