Question

Logarithms Equations.

Answer 1

\[\log_{6}(x+2)+\log_{6}(x-3)=1 \]

Answer 2

So we have logbase6(x^2-x-6)=1

Answer 3

then I get a little stuck

Answer 4

do we take the log of 1, as logbase6(1)

Answer 5

good now what is 6^1 = x^2 -x -6?

Answer 6

6, so I bring it over a factor the trinomial?

Answer 7

yes you will factor 0= x^2 -x -12...

Answer 8

x^2-x-12? And the reason it becomes an linear equation is because we took the same log bases?

Answer 9

Its not linear... But the law of logarithms is applied to get to the 6^1... the rest is the quadratic formula.

Answer 10

oh my mistake, but we can work with it because it has the same log bases

Answer 11

yes... complete the rest its easy...