Question

which equation is equivalent to \\(\log_{3}(x+5) = 2\\)?

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

Explanation:

⚡ Using what you learned: Logarithms and Exponential Equations

Step 1: Identify the logarithmic form

The given equation is:

$$ \log_{3}(x+5) = 2 $$

This is in the logarithmic form:

$$ \log_{b}(y) = x $$

where \( b = 3 \), \( y = x+5 \), and the exponent is \( 2 \).

Step 2: Convert to exponential form

Using the definition of a logarithm, \( \log_{b}(y) = x \) is equivalent to:

$$ b^x = y $$

Substituting our values into this definition:

$$ 3^2 = x+5 $$

Answer:

$$ 3^2 = x+5 $$