Question

Value of log(0.02)/(0.07)?

Answer 1

Well, is it `log\frac((0.02))((0.07))` or `log(0.02)/0.07`? Use your calculator.

`color(blue)(log\frac((0.02))((0.07))) = log(2/7) = log 2 - log 7`

`= 0.3010 - 0.8451 = color(blue)(-0.5441...)`

`color(blue)(log(0.02)/0.07) = (log(2cdot10^(-2)))/(7 cdot 10^(-2))`

`= (log2 - 2log10)/(7 cdot 10^(-2))`

`= (100log2 - 200log10)/7`

`= (30.10 - 200)/7`

`= 28/7 + 2.10/7 - 210/7 + 10/7`

`= 4.00 + 0.30 - 30.00 + 1.42857`

`= color(blue)(-24.27)`