Base e and Natural Logarithms

natural logarithm

exponential function

base logarithm

common logarithm

$$e^{\ln\left(50\right)}=x$$  

$$e^x=50$$  

$$e^{50}=x$$  

$$\ln\left(e^x\right)=50$$  

$$e^{\ln\left(x\right)}=8$$  

$$\ln\left(e^8\right)=x$$  

$$\ln x=8$$  

$$\ln8=x$$  

$$e^6\approx1.7918$$  

$$e^{\ln\left(6\right)}\approx1.7918$$

$$e^{1.7918}\approx6$$  

$$\ln\left(e^{1.7918}\right)\approx6$$  

$$\ln4=x$$  

$$\ln x=4$$  

$$e^{\ln\left(4\right)}=x$$  

$$\ln\left(e^x\right)=4$$  

$$\ln x=2$$  

$$\ln2=x$$  

$$x=2$$  

$$\ln x=e^2$$  

$$x=\ln12-5$$  

$$x=\frac{\ln22}{5}$$  

$$x=\frac{e^{12}}{5}$$  

$$x=\frac{\ln12}{5}$$  

$$x=\frac{e^1}{6}$$  

  $$x=\ln\left(1\right)+6$$  

$$x=\frac{\ln\left(1\right)}{6}$$   

$$x=e^1+6$$