Question

What is x if `log (x+4) - log (x+2) = log x`?

Answer 1

I found: `x=(-1+sqrt(17))/2~~1.5`

Explanation:

We can write it as:
`log((x+4)/(x+2))=logx`
to be equal, the arguments will be equal:
`(x+4)/(x+2)=x`
rearranging:
`x+4=x^2+2x`
`x^2+x-4=0`
solving using the Quadratic Formula:
`x_(1,2)=(-1+-sqrt(1+16))/2=`
two solutions:
`x_1=(-1+sqrt(17))/2~~1.5`
`x_2=(-1-sqrt(17))/2~~-2.5` which will give a negative log.