Logs

Luckily, for the MCAT, $logs$ are base 10. Below are some pearls to get you through log calculations:

• The log of 1 equals zero.
• The log of an exponent in scientific notation equals the exponent. For example, $log \ 10^{-4}$, equals -4.
• The $log \ 2 = 0.3$, $log \ 4 = 0.6$ and $log \ 8 = 0.9$.
  • Remember this by ``2, 4, 8 equals, 3, 6, 9''
• If a quantity is calculated through a $\log$ calculation, e.g. dB's (Sound chapter, p. ), then a 10-fold increase in dB's results in a 10-fold ($10^{1}$) increase in intensity, a 20-fold increase in dB's will result in a 100-fold ($10^{2}$) increase in intensity, a 30-fold increase in dB's will result in a 1000-fold ($10^{3}$) increase in intensity, etc.
• Placing a negative sign in front of the $\log$ of a decimal ensures that the answer will be positive. For example, in Equation 3.1 below, a negative sign is placed before the $\log$ because it has been agreed that the quantity for $pH$ is positive as seen in Equation 3.2:

  
  

  $$-log [H^{+}] + -log [OH^{-}] = 14$$ (4.1)

  
  

  
  

  $$pH + pOH = 14$$ (4.2)