D Deo3560 New member Joined Jul 30, 2010 Messages 23 Feb 26, 2011 #1 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
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
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Feb 26, 2011 #2 \(\displaystyle 6^{x-2}=4^{x}\) \(\displaystyle \frac{6^{x}}{36}=4^{x}\) \(\displaystyle \left(\frac{3}{2}\right)^{x}=36\) \(\displaystyle xln(\frac{3}{2})=2ln(6)\) \(\displaystyle x=\frac{2ln(6)}{ln(\frac{3}{2})}\)
\(\displaystyle 6^{x-2}=4^{x}\) \(\displaystyle \frac{6^{x}}{36}=4^{x}\) \(\displaystyle \left(\frac{3}{2}\right)^{x}=36\) \(\displaystyle xln(\frac{3}{2})=2ln(6)\) \(\displaystyle x=\frac{2ln(6)}{ln(\frac{3}{2})}\)
M Mrspi Senior Member Joined Dec 17, 2005 Messages 2,116 Feb 26, 2011 #3 Deo3560 said: 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 Click to expand... 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)
Deo3560 said: 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 Click to expand... 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)
