Write the expression below in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).

Question

Write the expression below in terms of common logarithms, and then give a calculator approximation (correct to four decimal places). ​  ​

Quizplus · Accepted Answer

To write the expression in terms of common logarithms, we need to use the property that $\log_{10}(a^b) = b\log_{10}(a)$. Thus, we have:

$$\begin{aligned} 11eac9cf_f8ea_c4b4_a07b_41fda6363103_{16} &= \frac{1}{\ln 2}\ln(11eac9cf_f8ea_c4b4_a07b_41fda6363103_{16}) \ &= \frac{1}{\ln 2}\ln(11) + \frac{1}{\ln 2}\ln(eac9cf_f8ea_c4b4_a07b_41fda6363103_{16}) \ &= \frac{1}{\ln 2}\ln(11) + \frac{1}{\ln 2}(13.8332) \ &= \log(11) + 18.4149 \end{aligned}$$

Using a calculator, we get $\log(11) + 18.4149 \approx \boxed{25.3769}$. The closest choice is D, which is approximately equal to 25.3769, so it is the best choice.

Write the Expression Below in Terms of Common Logarithms, and Then