Question

Determinati nr. nat. x din egalitatea:

[ ( $\frac{2}{3}$ )⁶ ]¹⁰ = [ ( $\frac{4}{9} }$ ) ⁵ ] la puterea x

Answer 1

2/3 la puterea 6 la puterea 10 = 2/3 la puterea 60

4/9 la puterea 5 inseamna 2/3 la puterea 2 la puterea 5 =2/3 la puterea 10

deci (2/3)^60=((2/3)^10)^x
(2/3)^60=(2/3)10x
10x=60
x=6