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Chapter 12: Problem 10

Write each equation in its equivalent logarithmic form. $$5^{4}=625$$

Short Answer

Expert verified
The equivalent logarithmic form of the equation \(5^{4} = 625\) is \( \log_{5}625 = 4\).

Step by step solution

01

Recognize the Exponential Equation

The given equation is in an exponential form as \(5^{4} = 625\). In this equation, 5 is the base, 4 is the exponent, and 625 is the result of the exponentiation.
02

Convert to Logarithmic Form

According to the definition of a logarithm, an equivalent logarithmic equation will be expressed as: 'Log base of the base equals the exponent', then we can write this as \( \log_{5}625 = 4\). The base of the logarithm is 5, which is the base in the original exponential equation, and the result of the logarithm is 4, which is the exponent in the exponential equation. The number to which we are applying the logarithm is 625, which is the result of the exponentiation in the original equation.

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Most popular questions from this chapter

Solve each equation. $$\log _{2}(x-3)+\log _{2} x-\log _{2}(x+2)=2$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can use any positive number other than 1 in the changeof-base property, but the only practical bases are 10 and \(e\) because my calculator gives logarithms for these two bases.

Write as a single term that does not contain a logarithm: $$e^{\ln 8 x^{5}-\ln 2 x^{2}}$$

$$\text { Solve: } \frac{x+2}{4 x+3}=\frac{1}{x}$$

Evaluate each expression without using a calculator. $$\log (\ln e)$$
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