Question

Hello, just got this question wrorg apparently, and would love to know why. It is:

simplify:

log(5/36) - log(5/9)

i did:

log5 - log4 + 2log3/log5 - 2log3 = -log4/-1 = log4

i got the -1 on the bottom from cancelling 2log3/-2log3

Any explanation would be great, thanks heaps.

Answer 1

rewrite the equation using log laws

\[\log( \frac{\frac{5}{36}}{\frac{5}{9}})\]

divide by a fraction invert and multiply

\[\log(\frac{5}{36} \times \frac{9}{5})\]

this gives
\[\log(\frac{1}{4})\]

use the log law for division

log(1) - log(4) = -log(4) since log(1) = 0

Answer 2

in your question you have

log(5) - log(36) - log(5) + log(9)

-2log(6) + 2 log(3) = -2log(2) - 2log(3) + 2log(3)

please note

= -2log(6) = 2(log(2 x 3)) = -2log(2) - 2log(3)

to the answer is -2log(2) or -log(2^2) or -log(4)