Problem 142 - College Algebra

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\).

Step-by-Step Solution

Answer

The statement '\(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\)' is true.

Step 1: Understand the statement

The claim is that \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\). This is essentially the definition of a logarithm where \(b\) is the base, \(x\) is the value and the result of the logarithm is the exponent.

Step 2: Verification

Based on the definition of a logarithm, the given statement is accurate. In other words, if \(b^y = x\), then \(\log _{b} x = y\).