Question

find the x intercept of the curve y=2log (√(x-1)-2)​

Answer 1

Answer:

The x-intercept has the form (c,0) where c is a constant.

So, set y = 0:

0=2log(x−2)+10=2log⁡(x−2)+1

⟹2log(x−2)=−1⟹2log⁡(x−2)=−1

⟹log(x−2)=−12⟹log⁡(x−2)=−12

Assuming that Assuming that

log(x−2)=loge(x−2)log⁡(x−2)=loge⁡(x−2)

then exponentiate to get: then exponentiate to get:

eloge(x−2)=e−12⟹eloge⁡(x−2)=e−12⟹

x−2=e−12⟹x−2=e−12⟹

x=2+1e12⟹x=2+1e12⟹

x=2+1e√≈2.60653066x=2+1e≈2.60653066

by calculator. So the x-intercept is

(2+e−12,0)≈(2.60653066,0).(2+e−12,0)≈(2.60653066,0).

This answer holds because

x≈2.60653066⟹x−2=2.60653066=0.60653066>0.x≈2.60653066⟹x−2=2.60653066=0.60653066>0.

The argument of a logarithm cannot be negative in the real numbers. If it is, then the logarithm is undefined.

Step-by-step explanation:

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