which expression results when the change of base formula is applied to $\\log_4(x + 2)$?\n$\\frac{\\log(x +…

which expression results when the change of base formula is applied to $\\log_4(x + 2)$?\n$\\frac{\\log(x + 2)}{\\log4}$\n$\\frac{\\log4}{\\log(x + 2)}$\n$\\frac{\\log4}{\\log x + 2}$\n$\\frac{\\log x + 2}{\\log4}$

which expression results when the change of base formula is applied to $\\log_4(x + 2)$?\n$\\frac{\\log(x + 2)}{\\log4}$\n$\\frac{\\log4}{\\log(x + 2)}$\n$\\frac{\\log4}{\\log x + 2}$\n$\\frac{\\log x + 2}{\\log4}$

Answer

Explanation:

Step1: Recall the change - of - base formula

The change - of - base formula for logarithms is (\log_{a}b=\frac{\log_{c}b}{\log_{c}a}), where (c>0,c\neq1). In the given logarithm (\log_{4}(x + 2)), if we choose the common logarithm (base (c = 10)), then (a = 4) and (b=x + 2).

Step2: Apply the formula

Substituting (a = 4) and (b=x + 2) into the change - of - base formula (\log_{a}b=\frac{\log_{c}b}{\log_{c}a}), we get (\log_{4}(x + 2)=\frac{\log(x + 2)}{\log4}) (since when (c = 10), (\log_{10}b=\log b) and (\log_{10}a=\log a)).

Answer:

(\frac{\log(x + 2)}{\log4}) (the first option)