Question

SOS determine o valor dos logaritmos a seguir

Answer 1

Explicação passo-a-passo:

a) Lembrando que:

$\boxed{\log_{a}(b.c)=\log_{a}b +\log_{a}c}$

Temos que $\log_{x}2=a$ e $\log_{x}5=b$.

Calculando $\log_{x}10$:

$\log_{x}10=\log_{x}(2.5)\\\\\log_{x}10=\log_{x}2+\log_{x}5\\\\\boxed{\boxed{\log_{x}10=a+b}}$

b)Lembrando que:

$\boxed{\log_{a}\bigg(\dfrac{b}{c}\bigg)= \log_{a}b-\log_{a}c}$

Temos que $\log_{x}7=20$ e $\log_{x}5=5$.

Calculando $\log_{x}(\frac{7}{5})$:

$\log_{x}\bigg(\dfrac{7}{5}\bigg)=\log_{x}7- \log_{x}5\\\\\log_{x}\bigg(\dfrac{7}{5}\bigg)=20-5\\\\\boxed{\boxed{\log_{x}\bigg(\dfrac{7}{5}\bigg)=15}}$

c)Lembrando que:

$\boxed{\log_{b}a=\dfrac{\log_{c}a }{\log_{c}b} }$

Convertendo $\log_{3}5$ para base 2:

$\boxed{\boxed{\log_{3}5=\dfrac{\log_{2}5}{\log_{2}3} }}$