Question

log 5 √5
log 4 1 por 2
log 25 125 ​

Answer 1

log 5 √5 = n

5ⁿ = √5

5ⁿ = 5¹/²

n = 1/2

log 4 1/2 = n

4ⁿ = 1/2

2²ⁿ = 2-¹

2n = -1

n = -1/2

log 25 125 = n

25ⁿ =125

5²ⁿ = 5³

2n = 3

n = 3/2

Answer 2

 Propriedades utilizadas:

$x^{-a}=\frac{1}{x^a}\\ \\x^{\frac{a}{b}}=\sqrt[b]{x^a}\\ \\Log_{x^b}y^a <=> \frac{a}{b}.Log_xy$

a -

$Log_5\sqrt{5}\\Log_55^{\frac{1}{2}}\\\frac{1}{2}.Log_55\\\frac{1}{2}.1\\\frac{1}{2}$

b -

$Log_4\frac{1}{2}\\Log_{2^2}2^{-1}\\\frac{-1}{2}.Log_22\\\frac{-1}{2}.1\\\-frac{1}{2}$

c -

$Log_{25}125\\Log_{5^2}5^{3}\\\frac{3}{2}.Log_55\\\frac{3}{2}.1\\\frac{3}{2}$

Dúvidas só perguntar XD