Question

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

Answer 1

`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.