Help me to solve this thx
Evaluate 6^x , given that 3^(x+1)*2^(2x+1)=2^(x+2)
Question: Given that $\displaystyle 3^{x+1}\times2^{2x+1}=2^{x+2}$,
Required to find $\displaystyle 6^x$
Solution: first of all simplify each index;
$\displaystyle 3^{x+1}\times2^{2x+1}=2^{x+2}$
$\displaystyle \Rightarrow 3^x.3^1\times2^{2x}.2^1=2^x.2^2$
$\displaystyle \Rightarrow 3^x.3^1\times2^x.2^x.2^1=2^x.2^2$
Try to work it out from there .... combine $\displaystyle 3^x$ with $\displaystyle 2^x$ to give $\displaystyle 6^x$ on the LHS and hence make $\displaystyle 6^x$ the subject of the formula and then simplify the terms on the RHS to give the required result of $\displaystyle 6^x=\frac{2}{3}$