Write each equation in its equivalent exponential form. 2 = log₃ x

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Recall the definition of logarithm: if \(y = \log_b x\), then the equivalent exponential form is \(b^y = x\).

Identify the base \(b\), the exponent \(y\), and the result \(x\) from the given equation \(2 = \log_3 x\).

Here, the base \(b\) is 3, the exponent \(y\) is 2, and the result \(x\) is the unknown value inside the logarithm.

Rewrite the logarithmic equation \(2 = \log_3 x\) in exponential form using the formula: \(3^2 = x\).

This expresses the original logarithmic equation as an exponential equation, which is the equivalent form requested.

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주요 개념

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Definition of Logarithms

A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log base 3 of x equals 2 means 3 raised to what power equals x. Understanding this definition is essential to convert between logarithmic and exponential forms.

Exponential Form of a Logarithmic Equation

The exponential form of a logarithmic equation log_b(x) = y is b^y = x. This equivalence allows rewriting logarithmic expressions as exponential ones, which is crucial for solving or simplifying equations involving logarithms.

Properties of Exponents

Exponents represent repeated multiplication of a base. Knowing how to interpret and manipulate expressions like b^y helps in understanding the relationship between logarithms and exponents, and in solving equations after conversion.

Write each equation in its equivalent exponential form. 2 = log3 x