Posted by **Roy** on Thursday, December 9, 2010 at 1:08am.

I am stuck solving this problem, any help please..Many thanks

find all numbers x that satisfy the given equation ln(2x)

------- =2

ln(3x)

- Pre-Calc -
**MathMate**, Thursday, December 9, 2010 at 8:22am
ln(2x)/ln(3x)=2

ln(2x)=2ln(3x)

ln(2x)=ln(9x²)

raise to power of e

e^{ln(2x)}=e^{ln(9x²)}

2x=9x²

x(9x-2)=0

x=0, or x=2/9

When working with log equations, always check back to see if the solution results in defined values.

Log(non-positive number) does not exist.

Check x=0:

Both log(2x) and log(3x) give undefined values, and

Lim x->0 log(2x)/log(3x)=1

and not 2 as required.

Check x=2/9:

log(2*x)/log(3*x)

=log(4/9)/log(6/9)

=log(4/9)/log(2/3)

=2log(2/3)/log(2/3)

=2 checks.

- Pre-Calc -
**Roy**, Thursday, December 9, 2010 at 11:37am
Thank you mathmate

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