Question

\[\log_{6}(a ^{2}+2)+\log_{6}2=2\]

Answer 1

$$
log_6(a^2+2)+log_6(2)=2\\
\implies log_6\pmatrix{(a^2+2)\times 2} =2 \implies log_6(2a^2+4)=2\\
\implies 6^{log_6(2a^2+4)}=6^2\\
\text{using the log cancellation rules}\\
\implies 2a^2+4 = 6^2
$$

Answer 2

and I think you can get it from there

Answer 3

Adding logarithms is the same as taking the logarithm of the product. You can rewrite that equation as \[\log_6(2(a^2+2)) = 2\]Then raise 6 to the power of each side, and remember that \(b^{\log_b a} = a\) so you have\[2(a^2+2) = 6^2\]

Answer 4

x=4

Answer 5

yes

Answer 6

and...

Answer 7

x=-4

Answer 8

right.