Condense
The number of logs you should end the problem with
one
multiple (2 or 3 for us depending on the question)
Expand: log(2xyz)
log2 + logx + logy + logz
Expand: log(4/x)
log4 - logx
What is the inverse of log5(x)
5x
Is this Condensed fully? If so, what did the student not do?
2log(xy)
No: Did not use Power Property
How many logs will be written at the end of the problem?
log9(x3/2y)
3 times
Condense: log8 + loga + logb
log(8ab)
Condense: log(10-x) - log(y)
log10-x/y
What is the inverse of 6x
log6(x)
log2(xy)-log(z)
Is the student correct? If not, what is the correct answer.
Not correct, the correct answer is log2(xy/z)
When expanding logarithms, where does the exponent go?
in the front of the log
Why can the product property not be applied to expand the following log
log(3x+1)
because you can not break apart logs that are adding or subtraction, only multiplying or dividing.
When you subtract the arguments, is the numerator or denominator being subtracted?
denominator
what is the inverse of 5x-1
log5(x)+1
A student wants to condense a logarithm, what steps should the student follow to do this (steps in order):
log7 + 2logx - log(3+y)
1) Power Property: logx^2
2) Product Property:log7x^2 - log3+y
3) Quotient Property: log7x^2/y
( 3 and 2 can technically be switched )
Steps in Order:
log(9x/z2)
1) Quotient Property: log(9x) - log(z2)
1) Product Property: log(9) + log(x) - log(z2)
3) Power Property: log(9) + log(x) - 2log(z)
How do you know when to use the Product Property?
Where there is multiplication/addition present.
How do you know when to use the Quotient Property?
Where division/subtraction is present.
what is the inverse of log4(x+2)
log(3x+1) - 3log4
log(9x+3)/4
log(x4y/z3)
4logx + ½log6y - 3log2z
Expand log(8x2y3)
log(8)+2log(x)+3log(y)
Which step should the Quotient Property be used when expanding (meaning there is a fraction in the argument)?
first
what is the inverse of ex
ln (x)
Note: it's an L not an I
natural log is Ln(x) or ln(x)