Logs and Exponentials

• What is e correct to two decimal places?


  2.72
• What is the value of log 1?


  0
• Which to coordinates will an exponential graph (base a) always pass through?


  (0, 1) and (1, a)
• Which two coordinates will a logarithmic graph (base a) always pass through?


  (1, 0) and (a, 1)
• LAWS OF LOGS: When you add two logs with the same base what happens?


  Multiply them
• LAWS OF LOGS: When you subtract two logs with the same base what happens?


  Divide them
• LAWS OF LOGS: How do you deal with a power inside of a log?


  Bring the power down to the front
• In an exponential equation, Ae to the power kt, what does A represent?

  The starting value
• In an exponential equation, Ae to the power kt, what does k represent?


  The percentage increase/decrease (as a decimal)
• What two letter abbreviation do we use for the logarithm to the base e?


  LN
• What is the inverse function of $y =$$a^x$?


  $y=$$logaX$
• What is the inverse funtion of $y=$$logaX$?


  $y =$$a^x$
• What is the inverse function of $y=$$e^x$?


  y = lnx
• What is the inverse function of y = lnx?


  $y=$$e^x$
• How do you solve an equation where x is a power? (eg. $4^x =$$10$)


  Take logs of both sides then bring x down the front.
• How do you solve an equation with a log on the left-hand side?


  Take powers of the right hand side
• How do you solve an equation containing the number e?

  By taking LN (Natural Log) of both sides