Question

determine the point of intersection

y=logbase 10(x-2)

and y=1-logbase 10(x+1)

Answer 1

A point of intersection is when the two equations equal each other. So set:

log(x-2) = 1 - log(x+1)

Then solve for x.

Does that help, or are the logarithms themselves giving you trouble?

Answer 2

log(x-2)= 1-log(x+1)

log(x-2)+log(x+1)=1

log(a)+log(b)=log(a*b)

log(x-2)+log(x+1)=log((x-2)*(x-1))

1=log(10)

log((x-2)*(x-1))=log(10)

So:
(x-2)*(x+1)=10

x^2-2x+x-2=10
x^2-x-2=10
x^2-x-2-10=0
x^2-x-12=0

Exact solutions of this equation is:
-3 and 4
Negative numbers have not logarithms.

So solution is x=4