You can use a calculator to create a table of values to check if this statement is true or false. Another way to think about this is to go back to the definition of logarithm: $\displaystyle{y}={\ln{{x}}}={\log}_{{e}}{x}\usepackage{cmbright}\Huge\$ means that $\displaystyle{{e}}^{{y}}={x}\usepackage{cmbright}\Huge\$ . As x decreases, the exponent y will decrease. This is the same as saying that as x decreases, $\displaystyle{\ln{{x}}}\usepackage{cmbright}\Huge\$ will decrease. In other words, as the input decreases, the graph goes down.