Question

questão logaritmo imagem abaixo

Answer 1

Explicação passo-a-passo:

Utilizaremos as seguintes propriedades logarítmicas:

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

Calculando $\log_{100}72$, sabendo que $\log2=0,3$ e $\log3=0,48$.

$\log_{100}72 =\dfrac{\log72}{\log100} \\\\\log_{100}72 =\dfrac{\log(8.9) }{2}\\\\\log_{100}72 = \dfrac{\log(2^{3} .3^{2} ) }{2}\\\\\log_{100}72 = \dfrac{\log2^{3} +\log3^{2} }{2}\\\\\log_{100}72 = \dfrac{3.\log2 +2.\log3 }{2}\\\\log_{100}72 =\dfrac{3.(0,3) +2.(0,48) }{2}\\\\log_{100}72 =\dfrac{0,9+0,96}{2}\\\\log_{100}72 =\dfrac{1,86}{2}\\\\\boxed{\boxed{log_{100}72 =0,93}}$