Question

log 9 1/27 =x
log 1/27
base 9
=x​

Answer 1

Explicação passo-a-passo:

$\sf \log_{9} \dfrac{1}{27} = x$

Converta na forma exponencial usando:

$\sf \log_{a} (b) = c~~\Rightarrow~~b = a^c$

$\sf \dfrac{1}{27} = 9^x$

$\sf (\dfrac{27}{1})^{-1} = (3^2)^x$

$\sf (3^3)^{-1} = 3^{2x}$

$\sf 3^{-3} = 3^{2x}$

$\sf \backslash \!\!\! 3^{-3} = \backslash \!\!\! 3^{2x}$

$\sf - 3 = 2x$

$\sf 2x = - 3$

$\boxed{\sf x = - \dfrac{3}{2}}$