Question

$2 log_{2}3 log_{3}5 - 4 log_{4}3$
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Answer 1

Resposta:

$\frac{2\ln \left(5\right)}{\ln \left(2\right)}-4\log _4\left(3\right) = 1.47393$

Explicação passo-a-passo:

$\mathrm{Aplicar\:as\:propriedades\:dos\:logaritmos}:\quad \log _a\left(b\right)=\frac{\ln \left(b\right)}{\ln \left(a\right)}$

$\log _2\left(3\right)\log _3\left(5\right)=\frac{\ln \left(3\right)}{\ln \left(2\right)}\cdot \frac{\ln \left(5\right)}{\ln \left(3\right)}$

$=2\cdot \frac{\ln \left(3\right)}{\ln \left(2\right)}\cdot \frac{\ln \left(5\right)}{\ln \left(3\right)}$

Simplificamos

$=2\cdot \frac{\ln \left(5\right)}{\ln \left(2\right)}$

$\mathrm{Multiplicamos\:as\:fracoes}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\ln \left(5\right)\cdot \:2}{\ln \left(2\right)}$

$=\frac{2\ln \left(5\right)}{\ln \left(2\right)}-4\log _4\left(3\right)$