Question

which expression results when the change of base formula is applied to \\(\log_{4}(x+2)\\)?

\\(\bigcirc \frac{\log(x+2)}{\log 4}\\)

\\(\bigcirc \frac{\log 4}{\log(x+2)}\\)

\\(\bigcirc \frac{\log 4}{\log x+2}\\)

\\(\bigcirc \frac{\log x+2}{\log 4}\\)

Explanation:

State the change of base formula

Using the Change of Base Formula knowledge point

$$ \log_b(a) = \frac{\log_c(a)}{\log_c(b)} $$

Apply the formula to the given expression

Using the Change of Base Formula knowledge point

$$ \log_4(x+2) = \frac{\log(x+2)}{\log 4} $$

Answer:

• (A) \(\frac{\log(x+2)}{\log 4}\) (Correct answer)
• (B) \(\frac{\log 4}{\log(x+2)}\)
• (C) \(\frac{\log 4}{\log x + 2}\)
• (D) \(\frac{\log x + 2}{\log 4}\)