Question

how would you solve:
x = 8^{log_{8} 4 + log_{8} 6}

Answer 1

first off
\[8^{\log_8(4)}=4\]

Answer 2

oh i should learn to read
it is
\[8^{\log_8(4)+\log_8(6)}\] right?

Answer 3

yes that is correct thank you

Answer 4

then you have a choice. you can write this as
\[8^{\log_8(24)}=24\]

Answer 5

or you can write it as
\[8^{\log_8(6)}\times 8^{\log_8(4)}=6\times 4=24\] either way

Answer 6

first method uses
\[\log(a)+\log(b)=\log(ab)\]and the second method pretty much explains why that is true

Answer 7

I was overlooking that property there, thank you!

Answer 8

yw