Question

Given log4=0.6021, log9=0.9542, and log12=1.-792, how do you find log 36?

Answer 1

Use one of the laws of logarithms: `log(a*b)=loga+logb.`
`log36=1.5563.`

Explanation:

We want to know `log36`, but we don't have a value for it. But we do have values for `log4`, `log9`, and `log12`. Can we use the above law of logarithms to find something equal to `log36`, in terms of the `log` values we're given?

Yes, we can! Because `36=4*9`, we can write:

`log36=log(4*9)`
`color(white)(log36)=log4+log9`
`color(white)(log36)=0.6021+0.9542`
`color(white)(log36)=1.5563`

So, based on the values given for `log4` and `log9`, we have:
`log36=1.5563.`

Bonus:

What this log rule states is that multiplying two numbers is equivalent to adding their logarithms. So, if you were asked to multiply two big numbers together very quickly, you could convert this to simple addition by converting the numbers to their logs with a log table, adding the logs, and converting the sum back using the same log table.

If you're interested, look up "log tables" and "slide rules". This is how multiplication was done in the 1950s and 60s, before pocket calculators were around.