Question

calcular o valor da expressão
log1/2 8-log4/3 27/64+ log2 1024

Answer 1

.S=log_{ \frac{1}{2}}8-log_{ \frac{4}{3} } \frac{27}{64}-log_{2}1024    

log_{ \frac{1}{2}}8 \\\\
8= (\frac{1}{2})^{x} =2^{3}=2^{-x} = x=-3   \\\\\\
log_{ \frac{4}{3} } \frac{27}{64}\\\\\
( \frac{27}{64} )=( \frac{4}{3})^{x} \\\\\
( \frac{3}{4})^{3}= ( \frac{4}{3} )^{x} \\\\\
( \frac{4}{3})^{-3} =( \frac{4}{3})^{x}\\\\
x=-3 \\\\\\
   log_{2}1024 \\\\\
1024=2^{x} \\\\\
2^{10}=2^{x} \\\\\
x=10 
  

S=-3-(-3)-10 \\\\
S=-3+3-10\\\\
S=-10