What I know
inverse- a function's inverse switches the x and y values. y=x.
inverse- a function is one-to-one when it passes the horizontal line test. this means the inverse is a function. therefore the original function and the inverse are both a function if the original function as well passes the vertical line test. A more non-graphical explanation is that the original function only has one value for every input. this also applies for the inverse the input most only have one output. this is when the function becomes one-to-one. in a table of values of the original function, shows any repeating y values then the function is not one-to-one.
inverse-the notation for inverse is f-1(x)
logs- logs are more confusing but i well try it. logs are used to find the power of a number or a variable.
logs- logs are written as log base answer
ex. equation form: 2x = 4
log form: log24
logs- the standard form logs is by using base of 10. also there is another shorthand which is ln (natural log). it is log with base of e. e stands for a number.
what i do not know
well I'm very confused with the way logs are found. how can a log be found not using a calculator. i also don't really understand how to graph log equations. i had trouble in #35 c2. I'm in the gray area concerning the logs. what should i need to know about logs.
PS. i tried. i have not done these problems for a long time
Subscribe to:
Post Comments (Atom)
the story about Davy crockett helped me a lot to understand logarithm. without using a calculator.. hmmm my mom told me that before.. they had books with Pages and pages of log tables. luckily we have the calculators now.
ReplyDeletei also had trouble with 35, 36 and pretty much the rest of the questions on C2.
i dont get how i can separate the x in number 35: e^(x) + e^(-x) = 3
its hard. it will take time and a lot of practice.
Rocio and Jesus helped me with #35, which is similar to 36 as well.
ReplyDeleteDo the reciprocal of e ^ -x to the original equation given to you.
Then, multiply both sides by e^x in order to get 1/e^x to become "1". Now you should have e^2x+1 = 3e^x.
Next you subtract 3e^x to both sides and get e^2x-3e^x+1= 0.
Now its in the format of a quadratic equation.
You then have to complete the square
Treat e^x as just x
After completing the square you get
3 +/- (square root) 5 / 2.
"After that you take the natural log of everything to cancel out the e and you have your answer"
It's easy finding logs and graphing them without a calculator. All you need to do is change it to exponential form which makes it a lot easier unless you're dealing with decimals then you might need a calculator.
ReplyDeletewell sir i'm not that good at explaining how to find logs but ill show you with an example.
ReplyDeletelog(x)=2
the base here is 10
all you have to do is set whats on the right side of the equal sign as the exponent of the base.
this makes it 10^2=x
10^2=100
therefore x=100
I hope thats what you needed
Well basically you can just plug in numbers you would desire and then if you need the inverse as well just switch the input and output(the x and y) its basically like an original equation just with log involved. Doubt I helped but I tried :).
ReplyDelete