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Chapter 12: Problem 39

Evaluate each expression without using a calculator. $$\log _{5} 5^{7}$$

Short Answer

Expert verified
The value of \( \log _{5} 5^{7} \) is 7.

Step by step solution

01

Identify the bases of the logarithm and the exponent

In the given expression \( \log _{5} 5^{7} \), both the base of the logarithm and the base of the exponent are 5.
02

Apply Basic Logarithm Principle

According to the basic principle of logarithms, if the base of the logarithm and the base of the exponent are the same, the logarithm simply evaluates to the actual exponent. Therefore, \( \log _{5} 5^{7} \) equals to 7.

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Most popular questions from this chapter

Solve each equation. $$5^{x^{2}-12}=25^{2 x}$$

a. Simplify: \(e^{\ln 3}\) b. Use your simplification from part (a) to rewrite \(3^{x}\) in terms of base \(e\)

What is an exponential equation?

Describe the change-of-base property and give an example.

Because the equations \(2^{x}=15\) and \(2^{x}=16\) are similar, I solved them using the same method.
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