help me solve this indices ASAP!!

**Joelyks** · October 29th 2009, 06:27 PM

Help me to solve this thx

Evaluate 6^x , given that 3^(x+1)*2^(2x+1)=2^(x+2)

**ibnashraf** · October 29th 2009, 07:26 PM

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 $6^x=\frac{2}{3}$

**Joelyks** · October 29th 2009, 07:34 PM

wow nice i got it thanks alot

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