ln(9x-1)=-4 solve for x?

Answer 1

ln(9x-1)=-4 means

e^(-4) = 9x -1, or

e^(-4) + 1 = 9x, divide both sides by 9

x = (e^(-4) + 1)/9 . Done.

Answer 2

To take the "natural" antilog of a value, you raise e to the power of that number.

for example, the antilog of 3 is e^3.

Taking the natural antilog of ln cancels the ln, leaving only the original number.

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Antilog of ln(x) = x

So, take the antilog on both sides.

ln(9x-1)=-4
antilog[ln(9x-1)] = antilog [-4]
(9x -1) = e^-4 = 1/e^4
9x = 1 + 1/e^4
x = 1/9 + 1/9e^4 = (e^4 + 1)/9e^4

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On many calculators, you can take the natural antilog of a number by entering the number, then pressing "Inverse" followed by "ln x"

4 "inv" "ln x" shows 54.59815 (same as e^4)

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I tend to disagree with daveg1222: if the explanation is clear enough, there will be some learning.

Teachers (good ones) can tell if a student understands or if he is just repeating what somebody else says, without any understanding.

Answer 3

x is -4 over 9

Answer 4

e^( - 4 ) = 9x - 1
9x = 1 + e^( - 4 )
x = (1/9) (1 + e^(- 4) )
x = (1/9) (1 + 1/e^4 )
x = 0.113

Answer 5

x = ((e^-4)+1)/9

Answer 6

you need to raise both sides to e

e^ln(9x-1)=e^4
9x-1=e^4
9x=1 +e^4
x= 1/9 + (e^4)/9

Answer 7

ln(9x-1)=-4

e^(-4) = 9x - 1

e^(-4) + 1 = 9x

x = [e^(-4) + 1]/9 or [(1 + e^4)/(9e^4)]

Answer 8

e^-4=9x-1
1/e^4+1=9x
x=1/(9e^4)+1/9