Question

Whats the y intercept of y= 1/2 log(x+1)-log(2x+10)

Answer 1

y = 1/2 log(x + 1) - log(2x + 10)

The y-intercept of any graph is the point where x=0.

y = 1/2 log(0 + 1) - log(0 +10)

y = 1/2 log(1) - log(10)

log(1) = 0
log(10) = 1

y = 1/2 (0) - 1

y = -1

That's all there is to it.  I'll bet you totally froze when you saw all those logs.

Answer 2

$y=\frac{1}{2}log(x+1)-log(2x+10)\\\\y\ intercept\ for\ x=0:\\\\\frac{1}{2}log(0+1)-log(2\cdot0+10)=\frac{1}{2}log1-log10=\frac{1}{2}\cdot0-1=-1\\\\Answer:y=-1,\ the\ point\ is\ (0;-1).$