Question

$3^{x+1} - 2*5^{x-2} = 5^{x} - 2*3^{x}$
Ребят, нужна ваша помощь

Answer 1

3ˣ⁺¹-2*5ˣ⁻²=5ˣ-2*3ˣ

3ˣ*3-2*5ˣ*5⁻²=5ˣ-2*3ˣ

3*3ˣ-2*5ˣ* 1/(5²)=5ˣ-2*3ˣ

3*3ˣ-2*5ˣ* 1/25=5ˣ-2*3ˣ

3*3ˣ- 2/25 *5ˣ=5ˣ-2*3ˣ

3*3ˣ+2*3ˣ=5ˣ+ 2/25 *5ˣ

5*3ˣ=27/25 *5ˣ

5*(3/5)ˣ=27/25

(3/5)ˣ=27/125

(3/5)ˣ=(3/5)³

х=3

Answer 2

$3^{x+1}-2cdot 5^{x-2}=5^{x}-2cdot 3^{x}\\3^{x}cdot 3-2cdot 5^{x}cdot frac{1}{25}-5^{x}+2cdot 3^{x}=0\\5cdot 3^{x}-(1+frac{2}{25})cdot 5^{x}=0; |:3^{x}\\ 5-frac{27}{25}cdot (frac{5}{3})^{x}=0\\(frac{5}{3})^{x}=5:frac{27}{25}\\(frac{5}{3})^{x}=frac{5cdot 25}{27}\\(frac{5}{3})^{x}=(frac{5}{3})^3\\x=3$