MATH HELP =) ln (3x+4) - ln (2x+1) = 5?

Question

if any1 is good at math can u explain to me how to go about this problem setp by step and what the final answer is?! Thanks!

Answer 1

ln (3x+4) - ln (2x+1) = 5
ln(3x+4)/(2x+1)= 5
(3x+4)/(2x+1) = e^5
3x+4 =2xe^5 + e^5
3x-2xe^5 =e^5-4
x(3-2e^5) = e^5-4
x = (e^5-4)/(3-2e^5)
x = -.4914915722

Answer 2

ln (3x + 4) - ln (2x + 1) = 5

First, you can combine the LN's.

ln a - ln b = ln (a/b)

So...
ln (3x + 4) - ln (2x + 1) = 5
becomes
ln [(3x + 4) / (2x + 1)] = 5

Now, take the e on both sides to get rid of the LN.

(3x + 4) / (2x + 1) = e^5
3x + 4 = e^5 (2x + 1)
3x + 4 = 2e^5 x + e^5
3x - 2e^5 x = (e^5) - 4
x(3 - 2e^5) = (e^5) - 4
x = [(e^5) - 4] / (3 - 2e^5) <--final answer

Answer 3

A property of the ln function is ln a - ln b = ln(a/b).
ln{(3x+4)/(2x+1)} = 5.

Also note: ln W = V means W = e^V

(3x+4)/(2x+1) = e^5

This time simply isolate x, cross-multiply first

3x+4 = [2e^5]x + e^5

(3 -2e^5)x = e^5 - 4

Thus x = {e^5 - 4} / (3 -2e^5)


d:

Answer 4

ln(3x+4)-ln(2x+1) = ln((3x+4)/(2x+1)) =

inside the ln you multiply the function in to 2 and divide it by 2:

ln( ((6x+8)/2) / (2x+1) ) = ln( ((6x+3+5)/2) / (2x+1) ) =

you seprate the parts inside the ln:

ln( ((6x+3)/2) / (2x+1) + (5/2) / (2x+1) ) =

ln( (6x+3) /(2*(2x+1)) + (5/2) / (2x+1) ) =

ln( (3*(2x+1))/(2*(2x+1)) + ((5/2)/(2x+1)) )




==> ln( 3/2+ ((5/2)/(2x+1)) ) = 5

==> 3/2 + ((5/2)/(2x+1)) = e^5 ==>(5/2)/(2x+1) = e^5 - 3/2

==> 5/2=(e^5-3/2) * (2x+1)

==> 2x+1 = (5/2)/(e^5 - 3/2) ==> 2x= (5/2)/(e^5 - 3/2) - 1

==>x= ((5/2)/(e^5 - 3/2) - 1) / 2

==> x= (5/4)/(e^5-3/2) - 1/2

Answer 5

ln [(3x+4)/(2x+1)] = 5 combine natural logs
e^5 = (3x+4)/(2x+1) convert to exponent form
3x+4 = e^5 (2x+1) multiply by 2x+1
3x+4 = 2e^5x+e^5 multiply the two terms out
3x-2e^5x = (e^5)-4 bring all the x terms to one side
x(3-2e^5) = (e^5)-4 factor out the x
x = (e^5-4)/(3-2e^5) divide to isolate the x

Answer 6

Simplify your logarithms

log(a) + log(b) = log(a*b)
log (a) - log(b) = log(a/b)

then

ln[(3x+4)/(2x+1)] = 5

exponentiate,

(3x+4)/(2x+1) = e^5
then solve for x

(3x+4) = e^5*(2x+1)
(3-2*e^5)*x = e^5-4

x = (e^5 - 4)/(3 - 2*e^5) ~ -0.491

Answer 7

Take the exp of both sides:
e^(ln(3x+4)-ln(2x+1)) = e^5
ln(a)-ln(b) = ln(a/b):
e^(ln((3x+4)/(2x+1))) = e^5
e^ln(x) = x:
(3x+4)/(2x+1) = e^5
3x+4 = (e^5)(2x+1) = 2xe^5 + e^5
x(3-2e^5) = e^5-4
x = (e^5-4)/(3-2e^5)

Answer 8

ln (3x+4) - ln (2x+1) = 5
ln[(3x+4)/(2x+1)]=5 {lna-lnb=lna/b}
(3x+4)/(2x+1)=e^5 {lnx=y=> x=e^y}
3x+4=2e^5x+e^5
(3-2e^5)x=e^5-4
x=(e^5-4)/(3-2e^5)