Question

question
write the log equation as an exponential equation. you do not need to solve for x.
\log_{4x} (5x - 9) = 2x - 1

Explanation:

Step1: Recall the logarithmic to exponential conversion formula

The general formula for converting a logarithmic equation \(\log_b a = c\) to its exponential form is \(b^c = a\), where \(b>0\), \(b
eq1\), and \(a>0\).

Step2: Apply the formula to the given equation

In the given equation \(\log_{4x}(5x - 9)=2x - 1\), we identify \(b = 4x\), \(a = 5x - 9\), and \(c = 2x - 1\).
Using the conversion formula, we substitute these values into \(b^c = a\) to get \((4x)^{2x - 1}=5x - 9\).

Answer:

\((4x)^{2x - 1}=5x - 9\)