Question

How do you solve `log_2x + log_2(x+2) = 3`?

Answer 1

I found: `x=2`

Explanation:

You can use a fundamental property of logs that tells us that:
`logx+logy=log(xy)`
to get:
`log_2[x(x+2)]=3`
now you use the definition of log to change into an exponential of the base and get:
`x(x+2)=2^3`
`x(x+2)=8`
rearranging:
`x^2+2x-8=0`
We can use the Quadratic Formula to find two values of `x`:
`x_(1,2)=(-2+-sqrt(4+32))/2=(-2+-sqrt(36))/2=(-2+-6)/2`
So:
`x_1=-4` NO you would get a negative argument for the log.
`x_2=2` YES