Logs and Powers

• What are powers useful for?

  Dealing with very large and very small numbers
• What does $X^2$ represent?


  <latex>X</latex squared or <latex>X</latex to the power of 2
• What is Avogadro's number?

  $6.022 \times 10^{23}$
• How is Avogadro's number expressed in full?

  602,200,000,000,000,000,000,000
• What does multiplying a number by itself many times mean?

  It represents powers of that number
• What is the base in powers?

  The number being multiplied
• What does the superscript number in powers indicate?

  The power or index of the base
• What is the result of $2^4$?


  16
• What is $3^3$ equal to?


  27
• What is $5^5$ equal to?


  3125
• What is the rule for multiplying powers with the same base?

  $a^n \times a^m =$$a^{n+m}$
• What is the rule for dividing powers with the same base?

  $a^n \div a^m =$$a^{n-m}$
• What does a negative power indicate?

  $a^{-n} =$$\frac{1}{a^n}$
• When do we typically use negative powers?

  In division of powers
• What is the priority of operations involving powers?

  Powers are prioritized before other operations
• What does $x^{1/n}$ represent?


  The nth root of $x$
• What is $a^{1/2}$ equal to?


  $\sqrt{a}$
• What is $a^{1/4}$ equal to?


  $4\sqrt{a}$
• What is the rule for powers of powers?

  $(a^n)^m =$$a^{n \times m}$
• What is the value of $5^{-4} \div 5^{-3}$?


  $5^{-1}$
• What is $(4^{-5})^3$ equal to?


  $4^{-15}$
• What is $6^{1/2} \div 6^{1/4}$ equal to?


  $6^{1/4}$
• What does $(8^{-6})^{1/2}$ equal to?


  $8^{-3}$
• What is the natural base number in life sciences?

  $e =$$2.7183$
• What does the number $e$ describe?


  Population growth, decay, and stability studies
• What is the formula for exponential growth?

  $n(t) =$$n_0 e^{rt}$
• What are the rules for using $e$ in calculations?


  $e^x \times e^y =$$e^{x+y}$
• What is the volume of a sphere formula?

  $V =$$\frac{4}{3} \pi r^3$
• What does the Arrhenius Equation describe?

  Rate of dissolution of a water-soluble polymer
• Why are powers useful in expressing numbers?

  They simplify large scale calculations
• What are logarithms related to?

  Powers and their inverses
• What is $10^3$ equal to?


  1000
• What does $y =$$a^x$ mean in logarithms?


  Logarithm to the base $a$ of $x$
• What is the logarithm of 1000 to the base 10?

  $Log_{10}(1000) =$$3$
• What is the logarithm of 2187 to the base 3?


  7
• What is the logarithm of 15625 to the base 5?


  6
• What is the logarithm of 128 to the base 2?

  7
• What is the logarithm of 245 to the base 10?

  $a =$$log_{10}(245) \approx 2.39$
• What is the log button on a calculator used for?

  Calculating logarithms
• What is the inverse function of the log button?

  Calculating exponentials