Problem 4 - College Algebra

Question

Write each equation in its equivalent exponential form. $$2=\log _{9} x$$

Step-by-Step Solution

Answer

The equivalent exponential form of the given logarithmic equation is \(9^2 = x\).

Step 1: Understanding Logarithm to Exponent Conversion

Recall that the logarithmic form \(b = \log_a x\) is equivalent to the exponential form \(a^b = x\). That means, the base of the logarithm becomes the base of the exponent, the output of the logarithm is the exponent, and the input to the logarithm is the result.

Step 2: Identifying the Parts of the Logarithm

In our given logarithm, \(\log_9 x = 2\), the base is \(9\), the output or the right side of the equation is \(2\), and the input or the argument of the logarithm is \(x\). So, in the exponential form, \(9\) would be the base, \(2\) would be the exponent, and \(x\) would be the result.

Step 3: Writing the Exponential Form

With all parts identified, we can now write the equation in the exponential form: \(9^2 = x\).