Question

qual o log 5 na base 625 raiz cubica de 25

Answer 1

$a^{x} =b \\ \\ log_{a} b=x \\ \\ log_{625 \sqrt[3]{25} } 5=x \\ \\ (625 \sqrt[3]{25} )^{x} =5 \\ \\ (5^{4} . (5^{2}) ^{ \frac{1}{3} }) ^{x} =5 \\ \\ (5^{4} (5)^{ \frac{2}{3} }) ^{x} =5 \\ \\ (5^{4+ \frac{2}{3} })^x =5 \\ \\ (5^{ \frac{14}{3} } )^x=5 \\ \\ (5)^{ \frac{14x}{3} } =5 \\ \\ \frac{14x}{3} =1 \\ \\ 14x=3 \\ \\ x= \frac{3}{14}$