Considere a função logarítmica dada por f(x) = 30 · [tex]2^{x}[/tex] , se f(x) for 600, qual será o valor de x?
a) [tex]\frac{4}{3}[/tex]
b) [tex]\frac{7}{3}[/tex]
c) [tex]\frac{10}{3}[/tex]
d) [tex]\frac{13}{3}[/tex]
e) [tex]\frac{16}{3}[/tex]
a) [tex]\frac{4}{3}[/tex]
b) [tex]\frac{7}{3}[/tex]
c) [tex]\frac{10}{3}[/tex]
d) [tex]\frac{13}{3}[/tex]
e) [tex]\frac{16}{3}[/tex]
Lista de comentários
[tex]\displaystyle \sf f(x) = 30\cdot 2^x \\\\\ 600 = 30\cdot 2^x \\\\ 2^x = \frac{600}{30} \\\\ 2^x= 20 \\\\ \log(2^x) = \log(20) \\\\ x \cdot \log 2=\log (2\cdot 10) \\\\ x\cdot \log 2= \log 2+\log 10 \\\\ x \cdot (0,3) =(0,3)+1 \\\\ x = \frac{1,3}{0,3} \\\\ \\ \large\boxed{\sf \ x = \frac{13}{3} \ }\checkmark[/tex]
letra d