Question

log 3 x + log 9 x^2 = 4

Answer 1

• Use as propriedades logarítmicas.

log3 x + log9 x^2 = 4

log3 x + 2log3^2 x = 4

log3 x + 2/2log3 x = 4

log3 x + log3 x = 4

2log3 x = 4

log3 x = 4/2

log3 x = 2

x = 3^2

x = 9

Resposta: x = 9

Answer 2

Explicação passo-a-passo:

$\sf log_{3}~x+log_{9}~x^2=4$

$\sf log_{3}~x+log_{3^2}~x^2=4$

$\sf log_{3}~x+\dfrac{2}{2}\cdot log_{3}~x=4$

$\sf log_{3}~x+1\cdot log_{3}~x=4$

$\sf log_{3}~x+log_{3}~x=4$

$\sf 2\cdot log_{3}~x=4$

$\sf log_{3}~x^2=4$

$\sf x^2=3^4$

$\sf x^2=81$

$\sf x=\sqrt{81}$

$\sf \red{x=9}$