Solve the equation:
[tex]e^x=0.5[/tex]
Since the variable is an exponent, we need to use logarithms. The base of the exponential is the number e, the base of the natural logarithms, thus:
[tex]\ln e^x=\ln0.5[/tex]
Applying the power rule for logarithms:
[tex]x\ln e=\ln0.5[/tex]
Since ln e = 1:
[tex]x=\ln0.5[/tex]
Using a calculator:
x = -0.69
