6^(x-2)=4^x

[Deo3560]

The problem is
6^(x-2)=4^x

The 4 choices are
x?6.26
x?7.48
x?9.12
x?8.84

Every time i do the problem I get
x?3.58

 

[galactus]

\(\displaystyle 6^{x-2}=4^{x}\)

\(\displaystyle \frac{6^{x}}{36}=4^{x}\)

\(\displaystyle \left(\frac{3}{2}\right)^{x}=36\)

\(\displaystyle xln(\frac{3}{2})=2ln(6)\)

\(\displaystyle x=\frac{2ln(6)}{ln(\frac{3}{2})}\)

 

[Mrspi]

The problem is
6^(x-2)=4^x

The 4 choices are
x?6.26
x?7.48
x?9.12
x?8.84

Every time i do the problem I get
x?3.58

First of all, my approach ends up with the same answer that Galactus got...I just went at it a bit differently.

Take the natural log of both sides:

ln 6[sup:254jeg4g](x - 2)[/sup:254jeg4g] = ln 4[sup:254jeg4g]x[/sup:254jeg4g]

(x - 2)*ln 6 = x ln 4

x*ln 6 - 2 ln 6 = x ln 4

get all terms containing x on the same side of the equation:

x ln 6 - x ln 4 = 2 ln 6

x (ln 6 - ln 4) = 2 ln 6

x = (2 ln 6) / (ln 6 - ln 4)