Straightening Curves with Logarithms

Logarithms turn powers and exponentials into linear relationships. All logarithm arguments must be positive. **Law** | **Take logarithms** | **Plot** | **Gradient** | **Vertical intercept** y=axn | lg y=lg a+nlg x lg y=nlg x+lg a | lg y against lg x | n | lg a y=abx | lg y=lg a+xlg b lg y=(lg b)x+lg a | lg y against x | lg b | lg a y=Aekx | ln y=ln A+kx ln y=kx+ln A | ln y against x | k | ln A y=axn: the graph of lg y against lg x is a straight line with gradient n and intercept lg a. y=abx: the graph of lg y against x is a straight line with gradient lg b and intercept lg a. Recovering constants lg a=c a=10c A=c A=ec **Read from the graph** | **Undo the logarithm** Vertical intercept =lg a | a=10intercept Gradient =lg b | b=10gradient Vertical intercept =ln A | A=eintercept Use the same logarithm base as the graph.