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

Verified step by step guidance

1. Recall the definition of logarithm: if \(y = \log_b x\), then the equivalent exponential form is \(b^y = x\).
2. Identify the base \(b\), the exponent \(y\), and the result \(x\) from the given equation \$2 = \log_3 x$.
3. Here, the base \(b\) is 3, the exponent \(y\) is 2, and the result \(x\) is the unknown value inside the logarithm.
4. Rewrite the logarithmic equation \$2 = \log_3 x\( in exponential form using the formula: \)3^2 = x$.
5. This expresses the original logarithmic equation as an exponential equation, which is the equivalent form requested.

Key Concepts

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.