Question

20^(3x+2)=4^(x+12)*5(5x-8) Помогите решить это показательная функция

Answer 1

20^(3x+2)= 4^(x+12)*5(5x-8)

4^(3x+2) * 5^(3x+2) =4^(x+12)*5(5x-8)

4²*4³ˣ * 5²*5³ˣ = 4¹²*4ˣ * 5⁻⁸*5⁵ˣ   сократим

4²ˣ*5¹⁰ =4¹⁰*5²ˣ

4²ˣ/5²ˣ = 4¹⁰/5¹⁰

(4/5)²ˣ=(4/5)¹⁰

2х=10

х=5

Answer 2

$20^{3x+2} = 4^{x+12}5^{5x-8},$
$4^{3x+2}5^{3x+2} = 4^{x+12}5^{5x-8},$
$4^{3x}4^{2}5^{3x}5^{2} = 4^{x}4^{12}5^{5x}5^{-8},$
$4^{2x}5^{10} = 4^{10}5^{2x},$
$( frac{4}{5}) ^{2x} = ( frac{4}{5}) ^{10},$
$2x = 10,$
$x = 5.$