Question 475740: y=2+log base 3 of(x-1)
1.) find the domain
2.)find the x-intercept
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! y=2+log base 3 of(x-1)
1.) find the domain
2.)find the x-intercept
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1) Domain:
The basic curve of log base 3 is shifted 1 unit to the right and bumped up 2 units. The bumping does not affect the domain but the asymptote (y-axis) is shifted 1 unit to the right.
Domain: (1, ∞)
..
2) x-intercept: set y=0, then solve for x
2+log3(x-1)=0
log3(x-1)=-2
convert to exponential form: (base(3) raised to log of number(2)=number(x-1)
3^-2=x-1
x=1+3^-2=1+1/9=10/9
x-intercept: 10/9
Check:
2+log3(x-1)
2+log3(10/9-9/9)
2+log3(1/9)
2+log3(3^-2)
2-2=0
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