Questions: Which equation is equivalent to log3(x+5) = 2? 3^2 = x+5

Which equation is equivalent to log3(x+5) = 2? 3^2 = x+5
Transcript text: Which equation is equivalent to $\log _{3}(x+5)=2$ ? $3^{2}=x+5$
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Solution

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Solution Steps

Step 1: Convert the Logarithmic Equation to Exponential Form

Given the logarithmic equation: \[ \log_{3}(x+5) = 2 \] we can convert it to its exponential form using the property that \(\log_b(a) = c\) is equivalent to \(b^c = a\). Therefore: \[ 3^2 = x + 5 \]

Step 2: Solve for \( x \)

Next, we solve the exponential equation for \( x \): \[ 3^2 = 9 \implies 9 = x + 5 \] Subtract 5 from both sides: \[ 9 - 5 = x \implies x = 4 \]

Final Answer

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

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