Question

log6(a^(2)+2)+log6(2)=2 help please

Answer 1

Possible intermediate steps:
(log(a^2+2))/(log(6))+(log(2))/(log(6)) = 2
Subtract (log(2))/(log(6)) from both sides:
(log(a^2+2))/(log(6)) = 2-(log(2))/(log(6))
Divide both sides by 1/(log(6)):
log(a^2+2) = (2-(log(2))/(log(6))) log(6)
Cancel logarithms by taking exp of both sides:
a^2+2 = 18
Subtract 2 from both sides:
a^2 = 16
Take the square root of both sides:
a = -4 or a = 4
Now test that these solutions are appropriate by substitution into the original equation:
Check the solution a = -4:
(log(a^2+2))/(log(6))+(log(2))/(log(6)) => (log(2))/(log(6))+(log(2+(-4)^2))/(log(6)) = (log(2))/(log(6))+(log(18))/(log(6)) ~~ 2.
So the solution is correct.
Check the solution a = 4:
(log(a^2+2))/(log(6))+(log(2))/(log(6)) => (log(2))/(log(6))+(log(2+4^2))/(log(6)) = (log(2))/(log(6))+(log(18))/(log(6)) ~~ 2.
So the solution is correct.
Thus, the solutions are:
a = -4 or a = 4