Question

log 81 base 3 + log 8 base 2

Answer 1

Explicação passo-a-passo:

Usando a definição de logaritmo:

$\log_{a} b=x \implies a^{x} =b$

Calculando $\log_{3}81$:

$\log_{3}81 =x\\\\3^{x}=81\\\\ 3^{x}=3^{4}\\\\\text Igualando\ os\ expoentes:\\\\x=4\\\\\therefore \boxed{\log_{3}81=4 }$

Calculando $\log_{2}8$:

$\log_{2}8=y\\\\2^{y}=8\\\\ 2^{y}=2^{3}\\\\\text Igualando\ os\ expoentes:\\\\y=3\\\\\therefore \boxed{\log_{2}8=3 }$

Calculando a soma:

$\log_{3}81+\log_{2}8=4+3\\\\\boxed{\boxed{\log_{3}81+\log_{2}8=7}}$