In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log9 x

Verified step by step guidance

1. Recall the definition of logarithm: $y=\log b_{}x$ means $b{y}^{}=x$.
2. Identify the base $b$, the exponent $y$, and the result $x$ from the given equation $2\; =\; \backslash ,\; \backslash log\_9\; x$.
3. From the equation, the base is $9$, the exponent is $2$, and the result is $x$.
4. Rewrite the logarithmic equation in exponential form using the definition: $9^2\; =\; x$.
5. This is the equivalent exponential form of the given logarithmic equation.

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 9 of x equals 2 means 9 raised to what power equals x. Understanding this definition is essential to convert between logarithmic and exponential forms.

Conversion Between Logarithmic and Exponential Forms

Logarithmic and exponential forms are two ways of expressing the same relationship. The equation log_b(x) = y is equivalent to the exponential form b^y = x. This conversion is key to rewriting logarithmic equations as exponential ones and vice versa.

Properties of Exponents

Exponents represent repeated multiplication of a base number. Knowing how to interpret and manipulate exponents helps in understanding the exponential form of logarithmic equations, such as recognizing that 9^2 means 9 multiplied by itself twice.