Logarithmic Function Manipulation

$$\log\left(x^5+y^6\right)$$

$$\log\left(x^5y^6\right)$$

$$\log\left(x^5-y^5\right)$$

$$\log\left(5x+6y\right)$$

$$\log_3\left(\frac{2\left(x+3\right)\left(x-1\right)}{\left(x+2\right)}\right)$$

$$\log_3\left(\frac{\left(x+3\right)\left(x-1\right)\left(x-1\right)}{\left(x+2\right)}\right)$$

$$\log_3\left(\frac{\left(x+3\right)\left(x-1\right)^2}{\left(x+2\right)}\right)$$

$$\log_3\left(\frac{\left(x+3\right)\left(x^2-2x+1\right)}{\left(x+2\right)}\right)$$

$$\frac{1}{2}\left(x-y\right)$$

$$\frac{1}{2}\left(xy\right)$$

$$\frac{1}{2}x+2$$

$$\frac{1}{2}\left(x+y\right)$$

0.8968

1.1134

1.5441

1.7961

$$\log_53+\log_5\left(4y\right)-\log_5\left(2z\right)$$

$$3+4\log_5y-2\log_5z$$

$$\log_53+4\log_5y-2\log_5z$$

$$\frac{\log_53\cdot\log_5y^4}{\log_5z^2}$$

$$2+\ln5-\frac{1}{2}\ln x$$

$$2\ln5-\frac{1}{2}\ln x$$

$$2+\ln5-2\ln x$$

$$2\ln5-2\ln x$$

$$\log\left(\frac{x^3+4}{y^2}\right)$$

$$\log\left(\frac{x^3}{4y^2}\right)$$

$$\log\left(\frac{4x^3}{y^2}\right)$$

$$\log\left(\frac{8x^3}{y^2}\right)$$

$$5\log x$$

$$\frac{\log5}{\log x}$$

$$\frac{\log x}{\log5}$$

$$\log x-\log5$$

$$\ln7-\ln3$$

$$\frac{\log_710}{\log_310}$$

$$\frac{\log3}{\log7}$$

$$\frac{\ln7}{\ln3}$$

$$\log_6\left(w-z^3\right)$$

$$\log_6\left(\frac{w}{z^3}\right)$$

$$\log_6\left(\frac{w}{z}\right)^3$$

$$\log_6\left(\frac{w}{z}\right)$$

$$\log_6\left(wz^3\right)$$