Question

Calcule o valor de cada expressão. *logaritmo*

Answer 1

Resposta:

Explicação passo-a-passo:

a)

$log_{3} \sqrt[4]{9}-4^{log_{4}5}=log_{3}(3^{2})^{\frac{1}{4}}-5=log_{3}3^{\frac{1}{2}}-5=\frac{1}{2}-5=\frac{1-2.5}{2}=\frac{1-10}{2}=-\frac{9}{2}$

b)

$2log_{9}1+[log_{0,5}(\frac{1}{8})]^{2}=2log_{9}9^{0}+[log_{\frac{1}{2}}(\frac{1}{2})^{3}]^{2}=2.0+[3]^{2}=0+9=9$

c)

$6^{2+log_{6}7}-log(log_{10})=6^{2}.6^{log_{6}7}-log1=36.7-log10^{0}=252-0=252$

d)

$4log_{8}2\sqrt{2}+log_{\frac{1}{5}}0,04=4log_{8}2.2^{\frac{1}{2}}+log_{\frac{1}{5}}\frac{4}{100}=4log_{8}2^{\frac{3}{2}}+log_{\frac{1}{5}}\frac{1}{25}=log_{8}(2^{\frac{3}{2}})^{4}+log_{\frac{1}{5}}(\frac{1}{5})^{2}=log_{8}2^{6}+2=log_{8}64+2=log_{8}8^{2}+2=2+2=4$