Question

write the log equation as an exponential equation. you do not need to solve for x. \\(\log_{(x - 3)}(2x + 2) = 5x\\)

Explanation:

Step1: Recall log to exponential conversion

The logarithmic equation \(\log_{b}a = c\) can be converted to the exponential equation \(b^{c}=a\), where \(b>0\), \(b
eq1\), and \(a>0\).

Step2: Apply the conversion formula

In the given equation \(\log_{(x - 3)}(2x + 2)=5x\), we identify \(b=(x - 3)\), \(a=(2x + 2)\), and \(c = 5x\). Using the conversion formula, we get \((x - 3)^{5x}=2x + 2\).

Answer:

\((x - 3)^{5x}=2x + 2\)