Evaluate log base 5 of 125

Problem

(log_5)(125)

Solution

1. Identify the base and the argument of the logarithm. The base is 5 and the argument is 125

2. Rewrite the argument as a power of the base. Since 5×5×5=125 we can write 125=5

3. Substitute the power back into the logarithmic expression to get (log_5)(5)

4. Apply the logarithm property (log_b)(bx)=x In this case, (log_5)(5)=3

Final Answer

(log_5)(125)=3

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