Question

Решите уравнение : 9^x+1 +3^2x+4=30

Answer 1

9 ^ ( Х + 1 ) + 3 ^ ( 2х + 4 ) = 30
( 3 ^ 2 ) ^ ( Х + 1 ) + 3 ^ ( 2х + 4 ) = 30
3 ^ ( 2х + 2 ) + 3 ^ ( 2х + 4 ) = 30
3 ^ ( 2х + 2 ) • ( 1 + 9 ) = 30
3 ^ ( 2х + 2 ) = 30 : 10
3 ^ ( 2х + 2 ) = 3 ^ 1
2х + 2 = 1
2х = - 1
Х = - 0,5

Answer 2

$9^{x+1}+3^{2x+4}=30\3^{2x+2}+3^{2x+4}=30\3^{2x}(3^2+3^4)=30\3^{2x}=frac{30}{3^2+3^4}=frac{30}{90}=frac{1}{3}\3^{2x}=3^{-1}\2x=-1\x=-frac{1}{2}$