Thursday

April 24, 2014

April 24, 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

**Related Questions**

Pre-Calculus - I need help solving this logarithmic equation: ln x + ln (x+3) = ...

Math - exponential function - Find all real numbers that satisfy (6^x)(7^(2x...

Math - Given the axioms: ln x = definite integral from 1 to x of 1/t dt ln e = 1...

Calc 121 - How do you integrate using substitution: the integral from 1 to 3 of...

calc - y=ln(x+1) +ln(x-1) find dy/dx I have trouble with this problem since i'm ...

Calc - a) y =ln(x-1) find dy/dx=? b) y=3 ln x - ln (1/x) where x >0, dy/dx...

Calc - y=ln(x+1) +ln(x-1) find dy/dx I have trouble with this problem since i'm ...

math - Express y as a function of x. C is a positive number. 3 ln y= 1/2ln (2x+1...

pre cal - (1/3)LN27 + 2LNx = LN(2-x) i think i just need help getting started. I...

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