Verified Answer :

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

AL2006

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.

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