Question

Question #39644

Answer 1

316227764.5

Explanation:

You need to know your log rules for this.

Let us simplify as much as we can.

`log(a) + log(b) = log (ab)`, this is true as long as they have the same base. (In this case, the base is 10)

So let us combine:
`log(x) +log(x+3) = 17`
`log(x*(x+3))=17`
`log(x^2+3x) = 17`

You also know this equation is of base 10 (If the base is not written, it is naturally assumed as base 10), so now we can write this in the exponential form.

`10^17 = x^2+3x`
`x^2+3x-10^17=0`

You now have a really nasty quadratics that is impossible to factor, but since you have the quadratic formula this is solvable.

`x = (-3 + sqrt(9+4*1*10^17))/2`
(Notice here I only used plus because you can't have a negative valued x in logs)

Plug it into your calculator, it should equal to 316227764.5

Hope that helps!