Question

Alguém me ajude com essas atividades da matéria '' logaritimo ''
to com uma grande dificuldade
*ignorem as respostas e respondam só as questões*

Answer 1

Obs.: Em uma proxima questão evite deixar dados pessoais!

1)

$log_{_{\frac{1}{9}}}\sqrt{3}=x\\\\\sqrt{3}=\left(\frac{1}{9}\right)^x\\\\3^{\frac{1}{2}}=\left(9^{-1}\right)^x\\\\3^{\frac{1}{2}}=\left(3^{-2}\right)^x\\\\3^{\frac{1}{2}}=\left(3\right)^{-2x}\\\\-2x=\frac{1}{2}\\\\x=-\frac{1}{4}$

2.

a)

$log\,1,5\\\\log\frac{3\;.\;5}{10}\\\\log\frac{3\;.\;\frac{10}{2}}{10}\\\\Utilizando\;as\;propriedades\;de\;log:\\\\(log3+(log10-log2))-log10\\\\(0,48+(1-0,30))-1\\\\(0,48+(0,7))-1\\\\1,18-1\\\\0,18$

b)

$log12\\\\log\,(2.2.3)\\\\log2+log2+log3\\\\0,30+0,30+0,48\\\\1,08$

c)

$log_32\\\\Utilizando\;troca\;de\;base:\\\\log_32=\frac{log_{10}2}{log_{10}3}\\\\log_32=\frac{0,30}{0,48}\\\\log_32=0,625$

3)

$2.log\,x=log\,9\\\\log\;x^2=log\,9\\\\log\;x^2=log\,3^2\\\\x=3$

4)

$pH=log\,\frac{1}{1x10^{-7}}\\\\pH=log\,10^7\\\\pH=7.log\,10\\\\pH = 7\;.\;1\\\\pH = 7$