Expand the Logarithmic Expression log base 5 of 125

Problem

(log_5)(125)

Solution

1. Identify the base and the argument of the logarithmic expression.

2. Rewrite the argument 125 as a power of the base 5

125=5

3. Substitute the exponential form back into the logarithm.

(log_5)(5)

4. Apply the property of logarithms that states (log_b)(bx)=x

(log_5)(5)=3

Final Answer

(log_5)(125)=3

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