Question

How to simplify log a^7 + 4log a^3 ?

Answer 1

\[\log_{a ^{7}} +4 \log_{a ^{3}} \]

Answer 2

remember the 3 log rules.

\[\log(a^7) + \log([a^3]^4) = \log(a^7) + \log(a^{12}) = \log(a^7a^{12}) = \log(a^{19}) = 19\log(a)\]

Answer 3

Are you sure of this \[ 4\log_{a ^{3}} = \log_{a ^{12}} \] ?

I thought it's equals to \[\log_{a ^{81}} \] isnt it ?

Answer 4

There is a difference between (a^3)^4 and a^(3^4)