Question

Write as the logarithm of a single quantity:1/3 log 8 – 2 log 4 + log 6 - 2 log 4 + log 6

Answer 1

1/3log8=log(2^3)^(1/3) =log2
2log4=log(2^2)^2=log2^4
log6=log6
2log4=log2^4
log6=log6

so your exercise after these will be

log2 - log2^4 + log6 - log2^4 + log6 = log(2/(2^4)) +2log6 -log2^4 =
=log(1/2^3) +log(36/2^4) = log(1/2^3) +log(36/16) =log(1/8) + log(9/4) =
= log(1/8 *9/4) =log(9/32)