Question

Номер 6.14 (г) наиподробнейшее решение.

Answer 1

$2\log_4x - \log_6x = 2\log_{\sqrt{6}}3$
$2*\frac{\ln(x)}{\ln(4)} - \frac{\ln(x)}{\ln(6)} = 2*\frac{ln(3)}{ln(\sqrt{6})}$
$\ln(x) * (\frac{2}{\ln(4)} - \frac{1}{\ln(6)}) = 2*\frac{ln(3)}{0.5*ln(6)}$
$\ln(x) = \frac{\ln(4)*\ln(6)}{\ln(6)*2 - \ln(4)} * 2*\frac{ln(3)}{0.5*ln(6)}$
$\ln(x) = \frac{\ln(4)*\ln(6)}{\ln(6)*2 - \ln(4)} * 2*\frac{ln(3)}{0.5*ln(6)} = \frac{4*\ln(3)*\ln(4)}{\ln(36) - \ln(4)}$
$\ln(x) = \frac{2*\ln(9)*\ln(4)}{\ln(36/4)} = 2*\ln(4) = \ln(16)$
$x = 16$