Posted by **Leanna** on Monday, September 6, 2010 at 11:39am.

Solve for x if 5+lnx=14/lnx.

- Calculus -
**MathMate**, Monday, September 6, 2010 at 1:06pm
substitute y=ln(x) ....(1)

to get

5+y=14/y

Solve the resulting quadratic equation in y.

Note that the domain of ln(x) is ℝ+\0, reject the value of y≤0.

Solve for x from (1) above.

- Calculus -
**Leanna**, Monday, September 6, 2010 at 6:45pm
ok, so i got e^-7 and e^2

does that mean i reject e^-7 because its less than or equal to 0?

- Calculus -
**MathMate**, Monday, September 6, 2010 at 7:40pm
Your answers are correct,

x=e^{-7} or x=e².

In fact, the value of y in y=ln(x) can be anything in ℝ, so your answers are correct. The restriction for non-negative values are on x only. My apologies.

## Answer this Question

## Related Questions

- Calculus 1 - Find the derivative of y with respect to x. y=(x^6/6)(lnx)-(x^6/36...
- calculus - sorry to ask a second question so soon, but i'm just not getting this...
- L'Hopital's rule - Find lim x->1+ of [(1/(x-1))-(1/lnx)]. Here is my work...
- math - how would you solve for y in this problem: ln(y-1)-ln2 = x +lnx ln(y-1)-...
- Calculus - Find the derivatives, dy/dx for the following functions. a. x^2y^4 = ...
- calculus - (a) find the intervals on which f is incrs or decrs. (b) find the ...
- calc - integral of 1 to e^4 dx/x(1+lnx) 1+lnx = a => dx/x = da dx/ x(1+lnx...
- math - I am suppose to simplify the following problems: sqrt(x)/x (isn't that ...
- Math (Calculus) - Can somebody solve this logarithm problem step by step for me ...
- Calculus - solve: 14. ln(1/x) = -2 16. lnx + ln(x+2) = ln(x+6) 22. ln(lnx) = 1