Question

How do you solve `log_3 (x + 3) + log_3 (x + 5) = 1`?

Answer 1

x=-2

Explanation:

`log(base3)(x+3)+log(base 3)(x+5)=1`-> use product rule of logarithm

log(base3)((x+3)(x+5))=1 write in exponential form

`3^1=(x+3)(x+5)`
`x^2+8x+15=3`
`x^2+8x+12=0`
`(x+6)(x+2)=0`

`x+6=0 or x+2=0`

x=-6 or x=-2

x=-6 is extraneous . An extraneous solution is root of transformed but it is not a root of original equation.

so x=-2 is the solution.