Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5^x=125

검증된 단계별 안내

Recognize that the equation is \(5^{x} = 125\). The goal is to express both sides as powers of the same base.

Recall that 125 can be written as a power of 5 because \(125 = 5^{3}\).

Rewrite the equation using this expression: \(5^{x} = 5^{3}\).

Since the bases are the same and the equation holds true, set the exponents equal to each other: \(x = 3\).

This gives the solution for \(x\) without needing to calculate any further.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

54s

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Exponential Equations

An exponential equation is one in which variables appear as exponents. Solving these equations often involves rewriting expressions so that both sides have the same base, allowing the exponents to be set equal to each other.

Expressing Numbers as Powers of the Same Base

To solve exponential equations, it is helpful to rewrite numbers as powers of a common base. For example, 125 can be expressed as 5³, which allows the equation 5^x = 125 to be rewritten as 5^x = 5^3.

Equating Exponents

Once both sides of an exponential equation have the same base, the exponents can be set equal to each other because if a^m = a^n, then m = n. This property simplifies solving for the variable in the exponent.

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5x=125