Question

write the exponential equation as a logarithmic equation. you do not need to solve for x.
$5^{x - 4} = 4x$
answer

Explanation:

Step1: Recall the exponential - logarithmic conversion rule

The general rule for converting an exponential equation \(a^{y}=x\) (where \(a > 0,a
eq1\)) to a logarithmic equation is \(\log_{a}(x)=y\).

In the given exponential equation \(5^{x - 4}=4x\), we have \(a = 5\), \(y=x - 4\) and \(x = 4x\) (using the general form \(a^{y}=x\)).

Step2: Apply the conversion rule

Using the rule \(\log_{a}(x)=y\) with \(a = 5\), \(x = 4x\) and \(y=x - 4\), we get \(\log_{5}(4x)=x - 4\).

Answer:

\(\log_{5}(4x)=x - 4\)