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Chapter 26: Problem 746

Write \(5^{3}=125\) in logarithmic form.

Short Answer

Expert verified
The exponential equation \(5^3 = 125\) in logarithmic form is \(\log_{5}(125) = 3\).

Step by step solution

01

Identify the Base, Exponent, and Result

In the exponential equation \(5^3 = 125\), we can identify the following: - Base: 5, which is the number that is raised to a power. - Exponent: 3, which is the power to which the base is raised. - Result: 125, which is the outcome of raising the base to the power of the exponent.
02

Write the Equation in Logarithmic Form

Based on the identified base, exponent, and result, we can write the logarithmic equation as: \[\log_{5}(125) = 3\] This logarithmic form indicates that the power (exponent) to which we must raise the base (5) to obtain the result (125) is 3.

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Most popular questions from this chapter

Find the values of the following logarithms: a) \(\log _{10} 10\) b) \(\log _{10} 100\) c) \(\log _{10} 1\) d) \(\log _{10} 0.1\) e) \(\log _{10} 0.01\)

Find \(4 \sqrt{36.91}\)

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