Step 1

The relationship between logarithmic and exponential function is given by

\(\displaystyle{{\log}_{{{b}}}{x}}={y}\Leftrightarrow{b}^{{{y}}}={x}\)

Where b is the base.

To convert exponential to logarithmic function find x, y, b and substitute in above equation.

Step 2

Given

\(\displaystyle{e}^{{{x}}}={2}\)

Here b=e, y=x, x=2.

So the logarithmic form is

\(\displaystyle{{\log}_{{{b}}}{x}}={y}\)

\(\displaystyle{\ln{{2}}}={x}\)

The relationship between logarithmic and exponential function is given by

\(\displaystyle{{\log}_{{{b}}}{x}}={y}\Leftrightarrow{b}^{{{y}}}={x}\)

Where b is the base.

To convert exponential to logarithmic function find x, y, b and substitute in above equation.

Step 2

Given

\(\displaystyle{e}^{{{x}}}={2}\)

Here b=e, y=x, x=2.

So the logarithmic form is

\(\displaystyle{{\log}_{{{b}}}{x}}={y}\)

\(\displaystyle{\ln{{2}}}={x}\)