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Math
second semester
| Question | Answer |
|---|---|
| Radicals: you add absolute value symbols to your answer when, | Whenever a variable comes out of a square root from an even power -when something is squared inside the radical -becuase Both positive and negative numbers give the same square, when you see an even square you dunno if x was positive or negative. |
| why do only even powers need absolute value symbols | Odd powers do not erase the sign: Because the sign is preserved, undoing an odd power does not need absolute value. |
| when solving exponential functions, how do you know when to put a +or- symbol in front your answer | You only use ± when undoing an even power. -if you are solving for the power tho (if the power is x) then there is only one root |
| continuous compounding formula | A = Pe^rt A = what you earn P = present value r= rate (change from % to decimal) t=time (yrs) |
| exponetial models | y= 0.001942e^0.00609x x = yrs |
| compound interest formula | A=P(1+nr)^nt n=number of times it's compounded |
| logarithmic form | LOGbase(answer)=exponent base = subscript ans= exponet |
| expodential form | LOGbase(exponent)=answer |
| Log1(3)=x | undefined |
| Log5(0)=x | undefined |
| 5Log5(1) = x | still zero, solve the larger chunk first (Log5(1) = x), then multiply the answer by 5 -DEAL WITH COEFFICENTS AT THE END |
| Log5(1)=x | x = 0 -aything to the power of 0 is1 |
| Log3(3) = x | 1 |
| 3(log)3 = x | anything times the log of itself is 1 |
| 3log3(5)= x | 5 |
| b^Logb(n)=n Logb(n) is all an exponet of b | n |
| write LogbMN the longer way | LogbM + LogbN multiplication = addition |
| LogbM/N | LogbM - LogbN division = subtraction |
| LogbM^k | exponets of logs and be brought to the front and multiplied to the rest of the expression K * LogbM |
| Log2(x+y) | can't be simplified (written in a different form) (only multiplication and division, not additon and subtraction) -+ and - can be solved tho so watch out |
| when asked to write something as a single log remember that | -fraction exponets must be written as radicals |
| steps to write something as a single log | 1. move exponets to the front 2. get rid of the radical 3. a log of the same thing is 1 |
| when you can use a calulator for logs | when the base is 10 --> common logs have a base of 10, it is implied |
| what are natural logs | logs with base e |
| what is the natural log of e | 1 |
| logb(n)=log(n) divided by log(b) | |
| ln(e^k) vs e^lnk | |
| 5Log5(1) = x and Log5(1^5) | these are equal |
| how to undo a log in a equation EX: log#=a | take whatever the other side &make it an exponent of the index for a basic log: 10^a |
| when you have the log of a binomial (solving for x not simplifying) log (a +or- b) | distribute the log aLog# +or- bLog# |
| what happens if you get a quadratic equation when dealing with logs | anything connected to the log must be greater than 0 (not = to) |
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Blessed Rectangle 10