The graph gets closer and closer to the y-axis, increases as the input increases, and curves downward. This is the general shape of the graph of any logarithm. The given graph passes through $\displaystyle{\left({0.5},{0}\right)}\usepackage{cmbright}\Huge\$ . You can check without using a calculator to see that this is a point on the graph of $\displaystyle{f{{\left({x}\right)}}}={\ln{{2}}}{x}\usepackage{cmbright}\Huge\$ . Also, because $\displaystyle{\ln{{e}}}={1}\usepackage{cmbright}\Huge\$ and $\displaystyle{e}\approx{2.7}\usepackage{cmbright}\Huge\$ then $\displaystyle{f{{\left({1.35}\right)}}}={\ln{{\left({2}\cdot{1.35}\right)}}}={\ln{{\left({2.7}\right)}}}\approx{1}\usepackage{cmbright}\Huge\$ , this function should also pass very close to $\displaystyle{\left({1.35},{1}\right)}\usepackage{cmbright}\Huge\$ . Other points can be checked with a calculator.