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

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