<s>[INST] Solution for $4^{2x+1}-3^{3x+1}=4^{2x+3}-3^{3x+2}$ I'm trying to get a solution for:
$4^{2x+1}-3^{3x+1}=4^{2x+3}-3^{3x+2}$
My main problem is that I don't know how to combine this potencys!
Ive also thought about another function that would bring me same difficulties:
$6^x=36*9.75^{x-2}$
What am I supposed to do?  
 [/INST] $$4^{2x+1}-3^{3x+1}=4^{2x+3}-3^{3x+2}$$
$$4^{2x+1}-4^{2x+3}=3^{3x+1}-3^{3x+2}$$
$$4\cdot4^{2x}-4^34^{2x}=3\cdot3^{3x}-3^23^{3x}$$
$$60\cdot4^{2x}=6\cdot3^{3x}$$
$$10\cdot4^{2x}=3^{3x}$$
$$10\cdot16^{x}=27^{x}$$
$$10=(27/16)^{x}$$
$$\log_{10} 10=\log_{10} (27/16)^{x}$$
$$1=x\log_{10}(27/16)$$
$$x=\frac{1}{\log_{10}27-\log_{10}16}$$
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