Question

Questão de Logaritmo 

Se $\frac{3}{Log _{2} x} + \frac{2}{Log _{3}x } + \frac{1}{Log _{5}x } = 2$, então quanto vale x²?

Answer 1

$Resolu\c{c}\~ao\to \left\{\begin{array}{ccc}\frac{3}{log_{2}x}+ \frac{2}{log_3x}+ \frac{1}{log_5x} = 2 \\\\ \frac{3}{ \frac{logx}{log2} } + \frac{2}{ \frac{logx}{log3} }+ \frac{1}{ \frac{logx}{log5} } = 2\\\\ \frac{3*log2}{logx} + \frac{2*log3}{logx} + \frac{1*log5}{logx} = 2\\\\3*log\ 2+2*log\ 3+log\ 5 = 2*log\ x \\\\log\ 2^3+log\ 3^2+log\ 5 = log\ x^2\\\\log\ (8*9*5) = log\ x^2\\\\\boxed{\boxed{x^2 = 360}} \end{array}\right$

Espero ter ajudado. :))