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Chapter 4: Problem 3

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$5^{x}=125$$

Short Answer

Expert verified
The solution for \(x\) in the equation \(5^{x}=125\) is \(x = 3\).

Step by step solution

01

Expressing both sides as a power of the same base

First, recall that 125 can be expressed as \(5^3\), because \(5*5*5 = 125\). So, rewrite the equation as \(5^{x}=5^3\).
02

Equating exponents

Since the bases on the left and right side of the equation are now the same, the exponents can be set equal to each other. This results in the equation \(x = 3\).
03

Confirming the solution

Check if \(x = 3\) is indeed a solution of the original equation. Substitute \(x = 3\) into the original equation: \(5^3 = 125\). Since both sides of the equation are equal, the solution is verified to be correct.

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Most popular questions from this chapter

Describe the following property using words: \(\log _{b} b^{x}=x\).

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