Question

18. Use common logarithms to approximate log,9 72 to four decimal places.

Answer 1

Answer:

$\log _972 = 1.9463$

Step-by-step explanation:

Given

$\log_972$

Required

Solve

Using the following laws of logarithm

$\log _ab = \frac{\log b}{\log a}$

We have:

$\log _972 = \frac{\log 72}{\log 9}$

Express 72 as 9 * 8

$\log _972 = \frac{\log (9 * 8)}{\log 9}$

So, we have:

$\log _972 = \frac{\log (9) + \log(8)}{\log 9}$

Split

$\log _972 = \frac{\log (9)}{\log 9} + \frac{\log(8)}{\log 9}$

$\log _972 = 1 + \frac{\log(8)}{\log 9}$

Express 8 and 9 as exponents

$\log _972 = 1 + \frac{\log(2^3)}{\log 3^2}$

This gives:

$\log _972 = 1 + \frac{3\log 2}{2\log 3}$

$\log 2 = 0.3010$

$\log 3 = 0.4771$

So, we have:

$\log _972 = 1 + \frac{3*0.3010}{2*0.4771}$

$\log _972 = 1 + \frac{0.9030}{0.9542}$

$\log _972 = 1 + 0.9463$

$\log _972 = 1.9463$