Question

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

Explanation:

Step1: Recall the logarithmic to exponential conversion formula

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

Step2: Identify the values of \(b\), \(x\), and \(y\) from the given logarithmic equation

In the given equation \(\log_{(x + 3)}(3)=2\), we have:

• The base \(b=x + 3\)
• The exponent \(x = 2\) (the value on the right - hand side of the logarithmic equation)
• The argument \(y = 3\) (the value inside the logarithm)

Step3: Apply the conversion formula

Using the formula \(b^{x}=y\), substitute \(b=x + 3\), \(x = 2\), and \(y = 3\) into it. We get \((x + 3)^{2}=3\)

Answer:

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