If log m (ab) = 4 and log m (a/b) = 12, then find log m a / log m b

Question

Hello! I would really appreciate some assistance in solving this problem algebraically. Thank you in advance!

Answer 1

Re write log (AB) as log a + log b= 4

Log(A/B) as log a - log b = 12

now add the 2 equations together

2log a = 16

log a= 8.

substitute value of log a back into either equation to solve for log b

8 + log b = 4

log b = -4

so log a/log b = 8/-4 = -2

Interesting way to make you use your log rules