Question

calcular o valor de:

a) 8^log de 5 na base 4

b) 9^2-log √2 na base 3​

Answer 1

Resposta:

Explicação passo-a-passo:

$a)log_{a}\frac{b}{c}=logb-logc\\\\2)kloga_{b}=logb^{k}\\\\3)log_{a^{x}b}=\frac{1}{x}log_{a}b\\\\4)a^{log_{a}b}=b\\\\a)8^{log_{4}5}=(2.4)^{log_{4}5}=2^{log_{4}5}*4^{log_{4}5}=2^{log_{2^{2}5}}*5=2^{\frac{1}{2}log_{2}5}*5=2^{log_{2}5^{\frac{1}{2}}}.5=5^{\frac{1}{2}}*5=5\sqrt{5}$\\\\\\b)$9^{2-log_{3} _{\sqrt{2}}}=(3^{2})^{2-log_{3}\sqrt{2}}=3^{4-2log_{3}\sqrt{2}}=3^{4-log_{3}\sqrt{2} ^{2}}=3^{4-log{_{3}2}}=\frac{3^{4} }{3^{log_{3}2}}=\frac{81}{2}$