the va's are where x is undefined, or where the denomenator is zero
first simplify if applicable
cannot simplify
set denom to zero
2x-5=0
2x=5
x=2.5
the vertical assemtote is vertical so it is x=2.5 or 5/2
the VA is x=5/2
The length of a rectangle is 1 units more than the width. The area of the rectangle is 72 units. What is the width, in units, of
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the va's are where x is undefined, or where the denomenator is zero
first simplify if applicable
cannot simplify
set denom to zero
2x-5=0
2x=5
x=2.5
the vertical assemtote is vertical so it is x=2.5 or 5/2
the VA is x=5/2
This equation uses two properties of logarithms:
So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15
So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15