# Logarithmic problem help

#### Nikhiln25

I have to solve x in terms of k

$$\displaystyle log x + log (x+9)=k$$

#### Also sprach Zarathustra

log(x) + log(y) = log(xy)

• HallsofIvy

#### Nikhiln25

log(x) + log(y) = log(xy)

Sorry wrote that completely wrong, meant to say solve for X in terms of K

#### HallsofIvy

MHF Helper
Yes, Also Sprach Zarathustra understood that. Apply his hint. If "log(x)+ log(y)= log(xy)" is a general rule, then what is log(x)+ log(x+ 9)?

Do you know how to solve log(y)= k for y? Do you know what the inverse function to log(x) is?

#### Nikhiln25

Yes, Also Sprach Zarathustra understood that. Apply his hint. If "log(x)+ log(y)= log(xy)" is a general rule, then what is log(x)+ log(x+ 9)?

Do you know how to solve log(y)= k for y? Do you know what the inverse function to log(x) is?
I haven't taken pre calc in 3 years so my memory of it is really sketchy..this is a review problem for calc which I'm taking right now.

Log(x^2+9x)=k
10^k=(x^2+9x)

Can't really figure out where to go from there. Like I said I barely remember anything from pre calc since its been about 3 years.

#### Bacterius

That's the right way to do it, now notice that it is equal to the equation $$\displaystyle x^2 + 9x - 10^k = 0$$, which is a quadratic equation in $$\displaystyle x$$ with a constant term in $$\displaystyle k$$. Therefore you can apply the quadratic formula to isolate $$\displaystyle x$$ and solve it in terms of $$\displaystyle k$$.