Friday

September 19, 2014

September 19, 2014

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

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

------- =2

ln(3x)

- Pre-Calc -
**MathMate**, Thursday, December 9, 2010 at 8:22amln(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 11:37amThank you mathmate

**Answer this Question**

**Related Questions**

Pre-Calc - I'm stuck on a pre-calc problem. I need to find y as a function of x...

Pre-Calc - Can you show me how to find the rectangular equation of r=2costheta...

Linear Equation - I posted a question below but forgot to put in the equation! ...

AP Calc Help!! - Let f be the function satisfying f'(x)=x√(f(x)) for all ...

Pre-CALC - Can anyone help me with this problem step by step please... Find the ...

Pre-Algebra - If the perimeter of a rectangle is 38 ft and the width is 9 ft, ...

URGENT!! PLEASE Calc - Verify that the function satisfies the three hypotheses ...

Pre-Calc - Please help me with this problem-I'm stuck (x-2)/(x+2) = (x+10)/x I'm...

calc - Verify that the function satisfies the three hypotheses of Rolle's ...

calc - Verify that the function satisfies the three hypotheses of Rolle's ...