Question

Calcule a soma de S
S = Log _{5} √5 + log _{9} √27 + log _{2} 128

Answer 1

$S=\log_5 \sqrt{5} +\log_9 \sqrt{27} +\log_2 128$

vou calcular separadamente depois a soma

$\log_5 \sqrt{5} =x \\ \\ 5^x= \sqrt{5} \\ 5^x=5^{ \frac{1}{2} } \\ \\ x= \frac{1}{2} \\ \\ \\ \log_9 \sqrt{27} =x \\ 9^x= \sqrt{27} \\ 3^{2x}=3^{ \frac{3}{2} } \\ \\ 2x= \frac{3}{2} \\ \\ x= \frac{3}{4} \\ \\ \\ \log_2 128=x \\ 2^x=2^7 \\ \\ x=7$

vamos agora a soma

$S= \frac{1}{2} + \frac{3}{4} +7 \\ \\ mmc(2,4)=4 \\ \\ S= \frac{2+3+28}{4} \\ \\ S= \frac{33}{4} ~~~~ou~~8,25$