Question

Qual é o valor de log3 9√27 ?
A) 2√ 27
B) 9
C) 5
D) 7/2
E) 1/2

Answer 1

.
$\log_39 \sqrt{27} =x \\ \\ 3^x=9 \sqrt{27} \\ \\ 3^x=3^2. \sqrt{3^3} \\ \\ 3^x=3^2.3^{ \frac{3}{2} } \\ \\ 3^x=3^{2+ \frac{3}{2} } \\ \\ 3^x=3^{ \frac{4+3}{2} } \\ \\ 3^x=3^{ \frac{7}{2} } \\ \\ x= \frac{7}{2} \\ \\ Letra~~D$

Answer 2

$\log_39 \sqrt{27}=\log_33^2 \sqrt{3^3}=\log_33^2.3^{\frac{3}{2}}=\log_33^{2+ \frac{3}{2}}=\log_33^ \frac{7}{2}= \frac{7}{2}.\log_33$$= \frac{7}{2}.1= \frac{7}{2}$ (Alternativa D)