Question

Sendo log 2 = 0,30 e log 3 = 0,48,Calcule:

Answer 1

Primeiro vamos fatorar os logaritmandos:

750 = 2 x 3 x 5³

18/15 = (2 x 3²) / (3 x 5)

a)

$log\;750\\\\log\;(2\;.\;3\;.\;5^3)\\\\log\;(2\;.\;3\;.\;(\frac{10}{2})^3)\\\\Utilizando\;as\;propriedades\;de\;log:\\\\log2+log3+3log(\frac{10}{2})\\\\log2+log3+3(log10-log2)\\\\0,30+0,48+3.(1-0,30)\\\\0,78+3.(0,7)\\\\0,78+2,1\\\\2,88$

b)

$log\left(\frac{18}{15}\right)\\\\log\left(\frac{2.3^2}{3.5}\right)\\\\log\left(\frac{2.3^2}{3.(\frac{10}{2})}\right)\\\\log(2.3^2)-log\left(3.(\frac{10}{2})\right)\\\\(log2+2log3)-\left(log3+(log10-log2)\right)\\\\(0,30+2\;.\; 0,48)-(0,48+(1-0,30))\\\\(0,30+0,96)-(0,48+0,7)\\\\1,26-(1,18)\\\\1,26-1,18\\\\0,08$