[tex]\boxed{x \approx 3.064}[/tex]
There is no general property that we can use to rewrite:
[tex]log_{a}(u\pm v)[/tex]
Then, we'll solve this problem graphically. Let's say that we have two functions:
[tex]f(x)=log(x+1) \\ \\ g(x)=-x^2 +10[/tex]
[tex]f(x)[/tex] is a logarithmic function translated one unit to the left of the pattern logarithmic function [tex]log(x)[/tex]. On the other hand, [tex]g(x)[/tex] is a parabola that opens downward and whose vertex is [tex](0,10)[/tex]. So:
[tex]f(x)=g(x)[/tex]
implies that we'll find the value (or values) where these two functions intersect. When graphing them, we get that this x-value is:
[tex]\boxed{x=3.064}[/tex]
Then, for [tex]x=3.064[/tex]:
[tex]f(x)=log(x+1) \\ \\ f(3.064)=log(3.064+1) \\ \\ f(3.064)=log(4.064) \\ \\ Using \ calculator: \\ \\ f(3.064) \approx 0.6 \\ \\ \\ g(x)= -x^2 +10 \\ \\ g(3.064)= -(3.064)^2 +10 \\ \\ g(3.064)=-9.388+10 \\ \\ g(3.064) \approx -0.6[/tex]