(7^3x)*7=5^x I can't figure out where to go from here, help please
U ugie New member Joined Apr 5, 2010 Messages 1 Apr 17, 2010 #1 (7^3x)*7=5^x I can't figure out where to go from here, help please
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Apr 17, 2010 #2 7(73x)=5x\displaystyle 7(7^{3x})=5^{x}7(73x)=5x 73x+1=5x\displaystyle 7^{3x+1}=5^{x}73x+1=5x (3x+1)log(7)=xlog(5)\displaystyle (3x+1)log(7)=xlog(5)(3x+1)log(7)=xlog(5) 3x+1x=log(5)log(7)\displaystyle \frac{3x+1}{x}=\frac{log(5)}{log(7)}x3x+1=log(7)log(5) 3+1x=log(5)log(7)\displaystyle 3+\frac{1}{x}=\frac{log(5)}{log(7)}3+x1=log(7)log(5) Now, finish solving for x?.
7(73x)=5x\displaystyle 7(7^{3x})=5^{x}7(73x)=5x 73x+1=5x\displaystyle 7^{3x+1}=5^{x}73x+1=5x (3x+1)log(7)=xlog(5)\displaystyle (3x+1)log(7)=xlog(5)(3x+1)log(7)=xlog(5) 3x+1x=log(5)log(7)\displaystyle \frac{3x+1}{x}=\frac{log(5)}{log(7)}x3x+1=log(7)log(5) 3+1x=log(5)log(7)\displaystyle 3+\frac{1}{x}=\frac{log(5)}{log(7)}3+x1=log(7)log(5) Now, finish solving for x?.