Question

(Mackenzie-SP) Supondo que log 2 = 0,3, a raiz da equação 2 - 40^6x = 0 é:

a) 1/32

b) 1

c) 6

d) 1/14

e) 1/16

Answer 1

Olá Maela,

vamos usar as seguintes propriedades de logaritmos:

$\begin{cases}logb^k~\to~k\cdot logb\\ log(bc)~\to~logb\cdot c~\to~logb+logc\\ log_kk=1\end{cases}$

$2-40^{6x}=0~~~~.\\ 2=40^{6x}\\ log2=log40^{6x}\\ log2=(log2^2\cdot10)^{6x}\\ log2=(2\cdot log2+log10)^{6x}\\ log2=6x\cdot(2log2+log10)~~~.\\\\ substituindo~os~valores~de~log,~e~lembre-se:~(log10=log_{10}10=1):\\\\ 0,3=6x\cdot(2\cdot0,3+1)\\ 0,3=6x\cdot(1,6)\\ 9,6x=0,3\\\\ x= \dfrac{0,3}{9,6}\\\\ x= \dfrac{0,3\cdot10}{9,6\cdot10}\\\\ x= \dfrac{3}{96}\\\\ x= \dfrac{3\div3}{96\div3}\\\\ x= \dfrac{1}{32}\\\\ \Large\boxed{\boxed{\boxed{S=\left\{ \dfrac{1}{32}\right\}}}}$

Portanto alternativa A

Tenha ótimos estudos ^^