How do you solve logx+log(x+1)=log6?

1 Answer
Jan 26, 2016

x=-3,2

Explanation:

Given equation is logx+log(x+1)=log6

I believe you're familiar with the basics of logarithm to know that there's a general identity, which is logm+logn=logmn

Now, we apply this general identity into the main equation, so we get logx(x+1)=log6. Sonce it's log on both sides, let's remove that to get
x(x+1)=6

Expand the left hand side and bring 6 to the left hand side, we get
x^2+x-6=0

I'm sure you know about quadratic equations to understand how I end up with a value of x now.