# can any one help i need to check if this is correct finding y explicitly as a function of x?

find y explicitly as a function of x express the equation in the form y=f(x) ln(3-y)=3ln(2x+1)-x heres my answer if any one can tell me if im correct and if im wrong can some one give me some help thanks.

ln(3-y)=3ln(2x+1)-x

exp ln(3-y)=exp 3ln(2x+1)-x

y=exp 3ln(2x+1)-x

=exp(ln(2x^3+1))

=exp (ln(2x^3+1))/exp

=2x^3+1/e

if any one can give me a few tips thanks.

### 3 Answers

- Alam Ko IyanLv 71 decade agoBest Answer
wait... i want to clarify...

is this

ln(3-y) = {3ln(2x+1)} - x

in such a case you cannot combine the 2nd term to the logarithmic term...

but some properties first...

n logA = log (A^n)

e^(A+B) = e^A*e^B

then

ln(3 - y) = {3ln(2x+1)} - x

ln(3 - y) = {ln(2x+1)^3} - x

e^ln(3-y) = e^[ {ln(2x+1)^3} - x ]

(3 - y) = e^ln[(2x+1)^3] e^(-x)

3 - y = (2x-1)^3 e^(-x)

y = 3 - {(2x-1)^3 e^(-x)}

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- Anonymous1 decade ago
hello! i think it should be looks that:

ln(3-y) = 3ln(2x+1)-x

exp ln(3-y) = exp [ 3ln(2x+1)-x ]

(3-y) = exp [ ln(2x+1)^3-x ]

where exp(b1)-exp(b2)=exp(b1)/exp(b2)

so

(3-y) = exp [ ln(2x+1)^3 ] / exp(x)

where exp(b)=e^b ,e^b=c where c is positive constant

so

3-y = (2x-1)^3 / e^x

y = 3-[ (2x-1)^3 / e^x ]

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