Question

47-48 Use formula 11 to evaluate each logarithm correct to six decimal places.

(a) \({\bf{lo}}{{\bf{g}}_{\bf{5}}}{\bf{10}}\)

(b) \({\bf{lo}}{{\bf{g}}_{\bf{5}}}{\bf{12}}\)

Short answer

a. 1.430677

b. 0.917600

Step-by-step solution

The formula 11 (Change of base formula)

Let b be any positive number. Then, the formula is shown below:

\({\log _b}x = \frac{{\ln x}}{{\ln b}}\)

Simplify the expression in (a)

Simplify the expression \({\log _5}10\) by using the formula 11.

\(\begin{aligned}{\log _5}10 &= \frac{{\ln 10}}{{\ln 5}}\\ &\approx 1.430677\end{aligned}\)

Thus, \({\log _5}10 \approx 1.430677\).

Simplify the expression in (b)

Simplfy the expression \({\log _5}12\) by using theformula 11.

\(\begin{aligned}{\log _5}12 &= \frac{{\ln 12}}{{\ln 5}}\\ &\approx 0.917600\end{aligned}\)

Thus, \({\log _5}12 \approx 0.917600\).