Resolver 2logx+2logz-4logy

$$2 \log x + 2 \log z - 4 \log y$$

Fatorizar

$$2\log_{10}\left(e\right)\left(\ln(x)+\ln(z)-2\ln(y)\right)$$

Passos Para a Resolução

Decomponha 2.

$$2\left(\log_{10}\left(x\right)+\log_{10}\left(z\right)-2\log_{10}\left(y\right)\right)$$

Considere \ln(x)\times \frac{1}{\ln(10)}+\ln(z)\times \frac{1}{\ln(10)}-2\ln(y)\times \frac{1}{\ln(10)}. Decomponha \frac{1}{\ln(10)}.

$$\frac{\ln(x)+\ln(z)-2\ln(y)}{\ln(10)}$$

Reescreva a expressão fatorizada completa.

$$\frac{2\left(\ln(x)+\ln(z)-2\ln(y)\right)}{\ln(10)}$$

Avaliar

$$2\log(e)\left(\ln(x)+\ln(z)-2\ln(y)\right)$$