• If $a^x=a^y$, then x=y when $a\ne 0,1,-1$.
• Converting between Exponential form and Logarithmic form
  • $x=a^y$ (a is the base, y is the exponent) is equivalent to $y=lo{g}_{a}x$ (a is the base, y is the exponent; x is the argument of the logarithm)
• When solving $32=2^x$, align the base number of both sides, like $2^5=2^x$, so x = 5
  • same applies to $-128=(-2{)}^{x-1}$, align the base => $(-2{)}^7=(-2{)}^{x-1}$, so 7 = x-1, x=8
• When graphing both the inverse function of an exponential function, remember to label both the functions separately
• Rewrite the inverse function equation to end when asked to determine the inverse of a function
• Application questions require a conclusion statement
• Remember to add a parenthesis if there are multiple factors within the log symbol ${\log }_3(x^2(x-1))$
• When solving x, Let $lo{g}_{}x...=t$
• Always write like $x{\log }_{}3$
• Do not include negative signs in the final answers
• For compounded interest, the t would be in years: $A_{final}=A_0(1+\frac{r}{n}{)}^{nt}$
  • t in years if not denoted specially
• For interest compounded continuously, it would be $A_{final}=A_0\ast e^{rt}$
  • t in years if not denoted specially
  • r could be positive or negative
• Growth and Decay: $A_{finalorwha{t}^{\prime }sleft}=A_0(C{)}^{\frac{t}{P}}$
• Application: when reaching certain years
  • the rule to round the previous digit up if more than 5 sometimes don't apply, as long as the digit is more than 0, it may need to round up the previous digit
• 750 seven hundred
• 3 Times Greater than, meaning 3 times as great as
• Challenge
  • Solve for x: $3^{lo{g}_{3}x}=x^{3+lo{g}_{x}4}$

Test

• (2) simplifying / solving with exponents
• (1) graphing exponential and/or logarithmic functions
• (5) simplifying / solving with logs
• (2) problem solving
  • earthquake Richter scale
  • compound interest
  • growth & decay