Question 24363: I need to find the domain, x-intercept, and vertical asymptote of the equation
y=-log3^x+2. First, i changed it into exponential form so that it was -3^y-2=x and tried to solve for the x-intercept. however, i got (-1/9,0) even thought the answer is supposed to be (9,0). Please help me, I need this answer today!
Thanks
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I need to find the domain, x-intercept, and vertical asymptote of the equation
y=-log3^x+2.THE ANSWER YOU GAVE AS 9 INDICATES THAT THE PROBLEM AS TYPED OUT BY YOU IS NOT CORRECT.IT SHOULD BE Y=2-LOG X TO BASE 3
THEN FOR X INTERCEPT ,WE PUT Y=0 AND SOLVE FOR X
0=2-LOG X TO BASE 3
LOG X TO BASE 3 =2
HENCE X=3^2=9
SO CORRECTING YOUR PROBLEM AS ABOVE ,LET US FIND DOMAIN OF X.
HERE THERE IS A LOG OF A FUNCTION X AND IT SHOULD BE ALWAYS POSITIVE. HENCE THE DOMAIN IS ALL REAL POSITIVE NUMBERS FOR X.
First, i changed it into exponential form so that it was -3^y-2=x
SO NOW YOU CAN SEE THAT Y=2-LOG X TO BASE 3
LOG X TO BASE 3 =2-Y
X=3^(2-Y)..SO WHEN Y=0 ,WE HAVE X=3^2=9 AS SHOWN ABOVE.
X=0 IS THE VERTICAL ASYMPTOTE SINCE WE FIND THAT LIMITING VALUE OF X =3^(2-Y)WHICH IS POSITIVE IS AS Y TENDS TO INFINITY X TENDS TO ZERO.
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