Question

calcule os logaritmos: ​

Answer 1

Explicação passo-a-passo:

Usando a definição de logaritmo:

$loga_{a}b=x\\ \\a^{x}=b$

f)

$log_{256} 128=x\\\\ 256^{x} =128\\\\(2^{8} )^{x} =2^{7} \\\\2^{8x} =2^{7} \\\\8x=7\\\\x=\frac{7}{8}$

g)

$log_{\frac{8}{27} } \frac{16}{81} =x\\\\(\frac{8}{27})^{x} =\frac{16}{81}\\\\((\frac{2}{3})^{3}) ^{x} =(\frac{2}{3})^{4} \\\\(\frac{2}{3}) ^{3x} =(\frac{2}{3})^{4} \\\\3x=4\\\\x=\frac{4}{3}$

h)

$log\sqrt[5]{100} =x\\\\10^{x} =\sqrt[5]{100}\\\\10^{x} =100^{\frac{1}{5} }\\ \\10^{x} =(10^{2} )^{\frac{1}{5} }\\ \\10^{x} =10^{\frac{2}{5} } \\\\x=\frac{2}{5}$

i)

$log_{0,5}0,125=x\\ \\(0,5)^{x} =0,125\\\\(0,5)^{x} =(0,5)^{3} \\\\x=3$