From the Jan 17 NYS Algebra 2 Regents, a multiple choice question with seemingly no satisfying answer:
"When $g(x) = \frac{2}{x+2}$ and $h(x) = \log (x+1)+3$ are graphed on the same set of axes, which coordinates best approximate their point of intersection?"
$$(1) \ (-0.9, 1.8)$$ $$(2) \ (-0.9, 1.9)$$ $$(3) \ (1.4, 3.3)$$ $$(4) \ (1.4, 3.4)$$
Plugging in an $x$ value of $-0.9$ yields $y$ values of $1.8181$... and $2$, respectively, so neither answers # 1 nor # 2 are 'best,' and an $x$-value of $1.4$ does not work at all for $g(x)$.
On Desmos I obtained an approximation of $(-.927, 1.8638)$ as the intersection of the graphs, i.e., approximately the 'solution.'
Here's my real question: can this type of equation, $\frac{2}{x+2} = \log(x+1)+3$ actually be solved algebraically; and if so, how?
Many thanks, as always.