# help me solve this indices ASAP!!

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• October 29th 2009, 07:27 PM
Joelyks
help me solve this indices ASAP!!
Help me to solve this thx :D
Evaluate 6^x , given that 3^(x+1)*2^(2x+1)=2^(x+2)
• October 29th 2009, 08:26 PM
ibnashraf
Question: Given that $3^{x+1}\times2^{2x+1}=2^{x+2}$,
Required to find $6^x$

Solution: first of all simplify each index;

$3^{x+1}\times2^{2x+1}=2^{x+2}$
$\Rightarrow 3^x.3^1\times2^{2x}.2^1=2^x.2^2$
$\Rightarrow 3^x.3^1\times2^x.2^x.2^1=2^x.2^2$

Try to work it out from there .... combine $3^x$ with $2^x$ to give $6^x$ on the LHS and hence make $6^x$ the subject of the formula and then simplify the terms on the RHS to give the required result of $6^x=\frac{2}{3}$
• October 29th 2009, 08:34 PM
Joelyks
wow nice i got it thanks alot :D:D:D:D