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| Question | Answer |
| Level: Basic Skill convert form: log_a (b)= y | a^y=b |
| Level: Difficult | Have a little conversation with yourself. How can we put 32 in terms of base 4 ? |
| Level: Medium | Have a little convo with yourself. Try something... perhaps with the squiggle trick? Or replacing something with "m" to make it a little nicer. x= 263 |
| This looks messy and scary. For your viewing pleasure, please put this into "Log" format. Level: Medium | Have a little convo with yourself. What kind of math tricks do you have up your sleeve to make this look better? |
| How can you be "confident" that you just rocked the last question? (And I didn't make a mistake in the answer?) Level: Easy | Check whether left equation is EQUAL to right. This will show that I made "legal" math moves to get from one equation to the next. |
| What are the "NPV"s or limitations of logs? For the equation below. Level: Important | X> 0, Y>0 and X cant be 1 |
| What are rational functions? Do you think you can sketch f(x) = (x^2+3x)/(x^3+2) ? Yes you can =) | An equation where there are "factors" on the top and bottom, that can be packed. They can originally look like polynomials on top and bottom of the fraction. |
| What do TOPs on rational functions tell us? f(x) = (x-2)(x-1) / (3-x) | TOPS make 1)Horizontal Asymptotes 2)ROOTS |
| What do BOTTOMs on rational functions tell us? f(x) = (x-2)(x-1) / (3-x) | 1) "POD" 2) Vertical Asymptotes |
| How do you know if there will be a 1)POD 2)Horizontal Asymptote 3) Vertical Asymptote? | 1) POD: IF there is a factor on bottom, that GETS cancelled 2) HA: On top, IF top and bottom has same degree 3) V.A.: IF there is a factor on bottom that DOESN'T cancel out |
| Given all that you know, sketch: (x-6)(x+1)/(3-x) | ... |
| Given all you know, get the equation for this. (The y-intercept is -1/5) | f(x) = 2x^2/ (x+5)(x-5) but need to include y-intercept... when x=0, y = -1/5 f(x) = (2x^2 +5)/(x+5)(x-5) |
| What is the formula for logs, generally used in word problems? | A=P(1+r)^t |
| If this is the general formula for a real life log question, what does each thing kind of mean? A=P(1+r)^t | A= Final amount P= Initial amount (1+R) = What is it doing to itself each time e.g. 'half-ing' itself each time would be 0.5 t = The number of times it (1+R)'s itself, like the number of times it "halves" itself. |
| What does a log graph generally look like, and what other "function" does it relate to, and what are some things to remember about logs? | 1. Climbing a hill. Invariant point at 1 with out translation. 2. INVERSE of an exponential function. (swap x and y) 3. Log of 1 is 0 |
| How can I find the inverse of an exponential function y=2^x | 1. Swap x and y (like all inverses...) x=2^y 2. Solve to get y= format... (but it's a variable in the exponent - so LOGS to the rescue) 3. answer: log2(x) = y |
| What is the general formula of a log, and what should I remember about vertical/horizontal shift and stretch for logs? | y=alog(x-h)+k |
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