Question

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

Answer 1

`\log _972 = 1.9463`

Explanation:

Given

`\log_972`

Required

Solve

Using the following laws of logarithm

`\log _ab = (\log b)/(\log a)`

We have:

`\log _972 = (\log 72)/(\log 9)`

Express 72 as 9 * 8

`\log _972 = (\log (9 * 8))/(\log 9)`

So, we have:

`\log _972 = (\log (9) + \log(8))/(\log 9)`

Split

`\log _972 = (\log (9))/(\log 9) + (\log(8))/(\log 9)`

`\log _972 = 1 + (\log(8))/(\log 9)`

Express 8 and 9 as exponents

`\log _972 = 1 + (\log(2^3))/(\log 3^2)`

This gives:

`\log _972 = 1 + (3\log 2)/(2\log 3)`

`\log 2 = 0.3010`

`\log 3 = 0.4771`

So, we have:

`\log _972 = 1 + (3*0.3010)/(2*0.4771)`

`\log _972 = 1 + (0.9030)/(0.9542)`

`\log _972 = 1 + 0.9463\\`

`\log _972 = 1.9463`