Question

4 la puterea 3x=8 la puterea10

Answer 1

$4^{3x}=8^{10}\Rightarrow(2^{2})^{3x}=(2^{3})^{10}\Rightarrow 2^{2*3x}=2^{3*10}\Rightarrow 2*3x=3*10\Rightarrow x=\frac{3*10}{2*3}=5$

Answer 2

"4 la puterea 3x = 8 la puterea10"

4³ x =8¹⁰ ⇔ x= 8¹⁰ : 4³     (*)

8¹⁰ =(2³)¹⁰ = 2³⁰

4³ =(2²)³ = 2⁶

Acum, relația (*) devine:

x = 2³⁰ : 2⁶ ⇔ x = 2²⁴