Question

Determine em cada item o valor de a:
a) log a 4=0,4
b) log a 8=-3/4
c) log a 7 = 1/2

Answer 1

$a)log_a4=0,4 \\ \\ a^{0,4}=4 \\ \\ (0,4 = \frac{2}{5} ) \\ \\ a^{ \frac{2}{5} }=4 } \\ \\ a= \sqrt[5]{4^2} \\ \\ a=4^{\frac{5}{2}}\\ \\a=32\\\\b)log_a8= \frac{-3}{4} \\ \\ a^{ \frac{-3}{4}}=8 \\ \\ a= \sqrt[4]{8^{-3}} \\ \\ a=8^{ \frac{4}{-3}} \\ \\ a= 0,0625\\ \\b)log_a7= \frac{1}{2} \\ \\ a^ \frac{1}{2} =7 \\ \\ a=7 ^{\frac{2}{1} } \\ \\ a=49$