Evaluate log base 125 of 5

Problem

(log_125)(5)

Solution

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

(log_125)(5)=x

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

125=5

3. Express the base 125 as a power of 5 to create a common base.

(5)x=5

4. Apply the power of a power rule for exponents.

5(3*x)=5

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_125)(5)=1/3

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