Question

Calcule o valor de LaTeX: \log_{\frac{1}{a^3}} a^{21} \ (a > 1)

Answer 1

$\log_{\frac{1}{a^3}} a^{21}=x \\\\21log_{\frac{1}{a^3}}a=x\\\\log_{\frac{1}{a^3}}a=\frac{x}{21}\\\\a=\frac{1}{a^3}^{\frac{x}{21}}\\\\a=a^{{-3}^{\frac{x}{21}}}\\\\a^1=a^{\frac{-3x}{21}}\\\\\frac{-3x}{21}=1\\\\-3x=21\\\\x = -\frac{21}{3}\\\\x=-7$