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Chapter 4: Problem 139

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.

Short Answer

Expert verified
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 by step solution

01

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.
02

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 \(\log_{4}{15}=x\).
03

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.

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