Question

Решите уравнение
3^(3x-1) +27^x = 2^(2x+1) +7×4^x

Answer 1

$3^{3x-1} +27^x= 2^{2x+1} +7*4^x \ \ 3^{3x-1} + 3^{3x} = 2^{2x+1} +7* 2^{2x} \ \ frac{3^{3x}}{3} +3^{3x}=2*2^{2x} +7*2^{2x} \ \ 4*3^{3x}=27*2^{2x} \ \ 2^{2x-2}=3^{3x-3} \ \ 2^{2(x-1)}=3^{3(x-1)} \ \ 4^{(x-1)}=27^{(x-1)} \ \ frac{4^{(x-1)}}{27^{(x-1)}} =( frac{4}{27} )^{(x-1)}=1=( frac{4}{27} )^0 \ \ x-1=0 \ \ x=1$