Logarithms Revision 5

LOGARITHMS Matthew Halls,Y12

WHAT ARE LOGARITHMS? „  If we want to find x in

!=​#↑% , we merely need to use #=√%&! .

„  But we can’t do this if the formula is

!=​%↑# .

„  We can use logarithms to find x in this case. „  The formula we want to use is

#=​log↓% ⁠! .

„  If l​ og⁠!  is used in an equation, assume it is l​ og↓%& ⁠! .

LOG LAWS „  Logarithms can be manipulated in a number of ways: „  ​log⁠!% =​log⁠! +​log⁠%  „  ​log⁠​!⁄%  =​log⁠! −​log⁠%  „  ​log⁠​!↑%  =%​log⁠!  „  ​log⁠√  %&!  =​log⁠! ⁄%  „  ​log↓! ⁠% =& „  ​log↓! ⁠! =% „  ​log↓! ⁠​!↑%  =%

QUESTION 1 „  ​*↑# =+ „  #=​log↓* ⁠+  „  #=,

QUESTION 2 „  ​log⁠%&​&↑#  =- „  #​log⁠%&& =„  #=​-⁄​log⁠%&&   „  #=*

QUESTION 3 „  .​&↑# =/ „  ​log⁠.​&↑#  =​log⁠/  „  #​log⁠.& =​log⁠/  „  #=​log⁠/ ⁄​log⁠.&  =&.-1/

QUESTION 4 „  √#&*& =. „  ​log⁠√,&20  =​log⁠.  „  ​log⁠*& ⁄# =​log⁠.  „  #=​log⁠*& ⁄​log⁠.  =%.+4