Question

matematică 30p
toate exercițiile vă rog
dau coroana ​

Answer 1

Răspuns:

Explicație pas cu pas:

1) a) 2log₃4 - 4log₃2 = log₃4² - log₃2⁴ = log₃(16/16) = log₃1 = 0

b) (log₃4 - log₃4/9) · log₅(∛5) = log₃(4·9/4) · log₅5¹⁽³ =

= log₃9 · 1/3·log₅5 = log₃3² · 1/3 ·1 = 2/3

2)

n=log₃2/1-log₃2/3+log₃4/3-log₃4/5+log₃6/5-log₃6/7+log₃8/7-log₃8/9

n = log₃[(2·4/3 ·6/5 ·8/7)/(2/3 ·4/5 ·6/7 ·8/9)]

n = log₃(384/105 ·945/384)

n = log₃(945/105) = log₃9 = log₃3² = 2log₃3 = 2 =>

n = 2 ∈ N

3) log₃2 = a

log₃216 = log₃(2³·3³) = log₃2³+log₃3³ =

= 3log₃2 + 3log₃3 = 3·(log₃2 + log₃3) =

= 3·(a+1) =>

log₃216 = 3·(a+1)