Problem 139 - College Algebra Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can solve \(4^{x}=15\) by writing the equation in logarithmic form.

Step-by-Step Solution

Answer

The statement makes sense because \(4^{x}=15\) can be re-written in logarithmic form as \(\log_{4}{15}=x\), which could be used to solve for x.

Step 1: Understanding the statement

To understand the given statement, we need to know about exponential equations and their logarithmic form. Here, \(4^{x}=15\) is an exponential equation where 4 is the base, x is the exponent and 15 is the result.

Step 2: Conversion to logarithmic form

The exponential equation \(4^{x}=15\) can be converted into a logarithmic form. In general, an exponential equation \(b^{y}=x\) can be expressed in logarithmic form as \(\log_{b}{x}=y\). Given this, we can rewrite \(4^{x}=15\) as \(\log_{4}{15}=x\).

Step 3: Verifying the statement

Since we have successfully converted the given exponential equation into its equivalent logarithmic form, the statement 'I can solve \(4^{x}=15\) by writing the equation in logarithmic form' makes sense.