Question

Calcule o logaritmo
Log 1,5 (4/9)

Answer 1

$log_{1,5}(\frac{4}{9})=x$

Aplicando a definição de logaritmos:

$(1,5)^{x}=\dfrac{4}{9}\\\\\\\left(\dfrac{15}{10}\right)^{x}=\dfrac{2^{2}}{3^{2}}\\\\\\\left(\dfrac{3}{2}\right)^{x}=\left(\dfrac{2}{3}\right)^{2}\\\\\\\left(\dfrac{3}{2}\right)^{x}=\left(\dfrac{3}{2}\right)^{-2}$

Bases iguais, iguale os expoentes:

$\boxed{\boxed{x=-2}}$

Answer 2

.
$\log_{1,5}{ \frac{4}{9}}=x \\ \\ (1,5)^x= \frac{4}{9} \\ \\ ( \frac{15}{10} )^x= \frac{4}{9} \\ \\ ( \frac{3}{2} )^x=( \frac{2}{3} )^2 \\ \\ ( \frac{3}{2} )^x=( \frac{3}{2} )^{-2 } \\ \\ x=-2$