Question

как решить?

3^{x-3} + 3^{x-2} = 4

Answer 1

(3^x)/27 + (3^x)/9 = 4,
(3^x)(1/27 + 1/9) = 4,
3^x = 27,
x = 3.

Ответ: 3.

Answer 2

$3^{x-3}+3^{x-2}=4$
$3^x:3^3+3^x:3^2=4$
$3^x*3^{-3}+3^x*3^{-2}=4$
$3^{-3}*3^x+3^{-2}*3^x=4$
$frac{1}{3^3} *3^x+ frac{1}{3^2} *3^x=4$
$frac{1}{27} *3^x+ frac{1}{9} *3^x=4$
$( frac{1}{27} + frac{1}{9} )*3^x=4$
$frac{4}{27} *3^x=4$
$frac{27}{4} * frac{4}{27} *3^x= frac{27}{4} *4$
$3^x=27$
$3^x=3^3$
$x=3$
Ответ: 3.