Quick!! Exponential/Logarithm Equation!!!

**Ultrafusion0** · February 21st 2008, 07:40 PM

Okay... Here's the question...

5^(x-2)=2^(3x+4)

Solve for x

Show steps plz

Thx in advance; i'm in a hurry!!!

**TheEmptySet** · February 21st 2008, 07:52 PM

$5^{x-2}=2^{3x+4}$
$ln(5^{x-2})=ln(2^{3x+4})$
$(x-2)ln5=(3x+4)ln2$
$xln5-2ln5=3xln2+4ln2$
$xln5-3xln2=4ln2+2ln5$
$x(ln5-3ln2)=4ln2+2ln5$

$x=\frac{4ln2+2ln5}{ln5-3ln2}$

**Ultrafusion0** · February 21st 2008, 08:01 PM

Thanks!!!
I never would've thought to do it THAT way...
Oh well... Thanks again!

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