advanced algebra question--logarithms question?

Question

ok, i have to solve for x;
lnx+ln(x+1)=2

i did the inverse of ln, e^x, to both sides and solved for x like any other algebraic equation.

though, i'm not getting the correct answer. i missed the classroom explanation on this section and the book doesn't provide examples for questions like these.

can someone please explain?
thanks in advance.

Answer 1

First combine into a single log: lnx + ln(x+1) = ln(x(x+1))

Then do e to both sides: e^(ln(x(x+1)) = e^2

On the left the e cancels ln and you have x(x+1) = e^2

This is x^2 + x - e^2 = 0

Now just do the Quadratic Formula

Answer 2

lnx+ln(x+1) = 2 so ln(( x*(x+1)) =2
so x(x+1)= e^2 and x^2 +x-e^2 =0 equation of 2nd degree

x= ((-1+-sqrt(1+4e^))/2 but you can´t use the minus sign of sqrt

because it would give you a negative value of x and negative numbers don´t have log

So your solution is x =(( -1+sqrt(1+4e^2))/2

Answer 3

ln(a)+ln(b) = ln(ab) for all positive a and b.

ln(x)+ln(x+1) = 2
ln(x^2+x)=2
e^2=x^2+x
Solve as a quadratic.

150 days of flood, that only works when one side of the equation is 0.

Answer 4

lnx + ln(x+1)=2

ln x(x+1)=2

x^2+x= e^2=7.389056099

x^2+x-7.389056099=0

x=-1/2+2.671901214i, -1/2-2.671901214i

Cheers

Answer 5

did you get something like 2.26? that should be right, as you can confirm by plugging it into the equation....

now for solving it... x(x+1) = e^2 is the equation you will need to solve. (or x^2 +x = e^2) (because adding logs is like multiplying!)

use the quadratic formula, if you are familiar with it.

so...

x = (-1+sqrt(1+4*e^2))/all over 2
and of course -1-sqrt....of the same thing

if i jotted it down correctly, that will be (-1+5.52)/2 or 2.26...


hope that helps!

Answer 6

remember that ln a + ln b = ln (ab)

therefore (x)(x+1) = e^2

x^2 + x - 7.389 = 0

use quadratic formula. Only positive root is used.

Answer 7

lnx+ln(x+1)=2
lnx(x+1)=lne²
x(x+1)=e²

x=e or x+1=e
x=e or x=e-1
x=2.718281828 or x=1.718281828

Answer 8

remember that ln a + ln b=ln (ab)

ln x + ln (x+1)=2
ln (x(x+1))=2
x(x+1)=e^2
x^2+x-e^2=0

x=(-1+/-√(1+4e^2))/2
x=(-1+/-√(30.56))/2
x=(-1-5.53)/2=-3.26
x=(-1+5.53)/2=2.26

x=2.26, -3.26

Answer 9

how are you?