Resolver 2logx+2logz-4logy

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

Factorizar

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

Pasos da solución

Factoriza 2.

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

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

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

Reescribe a expresión factorizada completa.

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

Calcular

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