Exponents and Logarithms Flashcards
Where does the f(x)=ex cross the y-axis?
It crosses at (0,1) since anything to the 0 power is 1.
How can you get rid of the coefficient of the log?
You push it to the exponent with the power rule.
What does it mean if the question says:
“Express f(x) in the form…”
It wants you to rearrange the function (which they will already have given you) so that it looks a certain way.
What are logs even good for?
They help you solve equations when you don’t know what’s in the exponent.
What does it mean if it says:
“Hence”
It means they want you to use the answer you just got for the last part to continue with this part of the question.
What is the range of the generic log functions, log(x) and ln(x)?
The range is all real numbers. The curve continues to infinity upwards and downwards.
How can you combine these logarithms?
You combine them together with the product rule.
What is the domain of any exponential function? (For example, ex or 3x or 5x.)
The domain is all real numbers. The curve continues to infinity left and right.
How can you expand this logarithm?
You expand it with the quotient rule.
What does it mean if it says:
“giving your answer as an integer”
It means that you know your final answer will just be an integer (which is a nice counting number but can be negative).
What is the domain of the generic log functions, log(x) and ln(x)?
The domain is x>0. The curve approaches a vertical asymptote on at x=0.
What does it mean if it says:
“Express ___ in terms of ___”
It means you should get the “express” thing alone, and all of the “terms of” will be on the right.
What does it mean if the question says:
“f(x) can be written as…”
It wants you to rearrange the function (which they will already have given you) so that it looks a certain way.
How are ex and ln(x) related?
They are inverses. This means each one undoes the other AND the graphs mirror over the diagonal.
What does it mean if a question says:
“Show that…”
It wants you to do that thing (e.g. find the inverse, find the vertex, find whatever), BUT it has already given you the answer you should get.
(So you’ll definitely know if you’ve gotten it right.)
Always use this shown thing in later parts of the question.
What can you do if you have two logarithms with different bases in the same equation?
You use the change-of-base formula.
How can you combine these logarithms?
You combine them together with the product rule.
What is the range of any exponential function? (For example, ex or 3x or 5x.)
The range is y>0. The curve approaches a horizontal asymptote on at y=0.
How do you get a variable you want out of an exponent?
You log both sides (using the same base as the exponent).
How can you get rid of the exponent on the m?
You bring it to the front with the power rule.
How can you expand this logarithm?
You expand it with the product rule.
What do you do if you’re supposed to find some unknown constant in a function?
You have to plug in some point. They will have somehow given you a point to plug in…(maybe with a graph, or talking about an inverse function)
What do you do if you need to solve an equation with a bunch of logs?
First, you need to get all the logs together.
Then you “kill” the log by using an exponent with the same base.
Where does the f(x)=ln(x) cross the x-axis?
It crosses at (1,0) since anything to the 0 power is 1.
What does it mean if a question says:
“Solve…”
You should isolate the variable.
Your answer will be:
x= or y= or whatever letter=
