Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 352: 37

a.) $x = e^3$ b.) $x = 2$

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\ln x = 3$ b.) $\ln e^2 = x$ a.) $\ln x = 3$ Rewrite the natural log form to exponential form: $\ln a = b \rightarrow e^b = a$ [Note: e stands for euler's number, NOT a variable] $\ln x = 3 \rightarrow e^3 = x$ $x = e^3$ b.) $\ln e^2 = x$ Bring the square to the front of the logarithm $2\ln e = x$ $2\times1 = x$ [Note: $\ln e = 1$] $x = 2$