Question

CALCULE OS LOGARÍTIMOS USANDO AS PROPRIEDADES

a) log81 27

b) log 128 32

c) log 625 25

d) log 343 49

e) log16 1 64

Answer 1

$\boxed{\log_{b^m}{a^n}=\dfrac{n}{m}\log_b{a}}$

a)

$\log_{81}{27}=\log_{3^4}{3^3}=\dfrac{3}{4}\log_3{3}=\boxed{\dfrac{3}{4}}$

b)

$\log_{128}{32}=\log_{2^7}{2^5}=\dfrac{5}{7}\log_2{2}=\boxed{\dfrac{5}{7}}$

c)

$\log_{625}{25}=\log_{5^4}{5^2}=\dfrac{2}{4}\log_5{5}=\boxed{\dfrac{1}{2}}$

d)

$\log_{343}{49}=\log_{7^3}{7^2}=\dfrac{2}{3}\log_7{7}=\boxed{\dfrac{2}{3}}$

e)

$\log_{16}{\dfrac{1}{64}}=\log_{2^4}{2^{-6}}=-\dfrac{6}{4}\log_2{2}=\boxed{-\dfrac{3}{2}}$