Question

which expression can be used to approximate the expression below, for all positive numbers \\(a\\), \\(b\\), and \\(x\\), where \\(a \
eq 1\\) and \\(b \
eq 1\\)?

\\(\log_a x\\)

• \\(\frac{\log_b x}{\log_b a}\\)
• \\(\frac{\log_b a}{\log_b x}\\)
• \\(\frac{\log_b b}{\log_x b}\\)
• \\(\frac{\log_a x}{\log_b x}\\)

Explanation:

Apply the change of base formula

$$ \log_{a}x = \frac{\log_{b}x}{\log_{b}a} $$

Answer:

• \(\frac{\log_{b}x}{\log_{b}a}\) (Correct answer)
• \(\frac{\log_{b}a}{\log_{b}x}\)
• \(\frac{\log_{b}b}{\log_{x}b}\)
• \(\frac{\log_{a}x}{\log_{b}x}\)