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 nonnegative values are on x only. My apologies.
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