Logarithms AS Physics Skills

Homework Complete logarithms homework sheet.

Learning Objectives To learn how to use logarithms to solve equations. To learn how to use logarithms to solve equations.

Logarithms 100 = = 10 2 In this statement we say that 10 is the base and 2 is the power or index. In this statement we say that 10 is the base and 2 is the power or index. Logarithms provide an alternative way of writing a statement such as this. We rewrite it as Logarithms provide an alternative way of writing a statement such as this. We rewrite it as log = 2 log = 2 This is read as ‘log to the base 10 of 100 is 2’. This is read as ‘log to the base 10 of 100 is 2’.

Logarithms

Logarithms I like to think of log b a as meaning I like to think of log b a as meaning “what power of b is a?” “what power of b is a?” So log translates to:- So log translates to:- “what power of 10 is 10,000?”  =4 “what power of 10 is 10,000?”  =4 So log 3 27 translates to:- So log 3 27 translates to:- “what power of 3 is 27?”  =3 “what power of 3 is 27?”  =3

Another Example 2 5 = = 32 we can write this as we can write this as log 2 32= 5 log 2 32= 5 Here the base is 2 and the power is 5. We read this as ‘log to the base 2 of 32 is 5’. Here the base is 2 and the power is 5. We read this as ‘log to the base 2 of 32 is 5’.

e e is a special number, a bit like π e is a special number, a bit like π It has the property that if you plot y=e x, then at every point on the curve the slope also equals the y-value It has the property that if you plot y=e x, then at every point on the curve the slope also equals the y-value For example, if x=5, then y=e 5 and the slope at that point, =e 5. For example, if x=5, then y=e 5 and the slope at that point, =e 5. e = e =

Log Rule 1 Example with Numbers:-

Log Rule 2 Examples with Numbers:- Examples with Numbers:-

Log Rule 3 Examples with Numbers:- Examples with Numbers:-

Log Rules Examples with Numbers:- Examples with Numbers:-

Inverse Logs Examples with numbers:- Examples with numbers:-

Standard Bases In Science, we tend to use only two bases either log to the base 10, which is written as just “log” or as “lg”. In Science, we tend to use only two bases either log to the base 10, which is written as just “log” or as “lg”. Or we use log to the base e (natural logarithm), which is written as “ln”. Or we use log to the base e (natural logarithm), which is written as “ln”. Similarly, Similarly,

Solving Equations For example, say we want to find x for:- For example, say we want to find x for:- Log both sides:- Log both sides:- Using log rule No.3:- Using log rule No.3:- Re-arranging:- Re-arranging:-