Question

solve log(x+1)= -x^2 +10

Answer 1

Answer:

$\boxed{x \approx 3.064}$

Step-by-step explanation:

There is no general property  that we can use to rewrite:

$log_{a}(u\pm v)$

Then, we'll solve this problem graphically. Let's say that we have two functions:

$f(x)=log(x+1) \\ \\ g(x)=-x^2 +10$

$f(x)$ is a logarithmic function translated one unit to the left of the pattern logarithmic function $log(x)$. On the other hand, $g(x)$ is a parabola that opens downward and whose vertex is $(0,10)$. So:

$f(x)=g(x)$

implies that we'll find the value (or values) where these two functions intersect. When graphing them, we get that this x-value is:

$\boxed{x=3.064}$

Then, for $x=3.064$:

$f(x)=log(x+1) \\ \\ f(3.064)=log(3.064+1) \\ \\ f(3.064)=log(4.064) \\ \\ Using \ calculator: \\ \\ f(3.064) \approx 0.6 \\ \\ \\ g(x)= -x^2 +10 \\ \\ g(3.064)= -(3.064)^2 +10 \\ \\ g(3.064)=-9.388+10 \\ \\ g(3.064) \approx -0.6$