i need math help please! 
?
can you explain how or why you get the following answers..
Which is the logartihmic form of 210 = 1024?
Correct Answer:
log21024 = 10
Express 2log 4 + 3log 2 as a single logarithm.
Correct Answer:
log 128
Ted's comic book collection, which was worth $1300 five years ago, has been increasing in value by 12% per year since then. Which expression gives the current value of the collection?
Correct Answer:
1300(1.12)5
Which statement is NOT always true?
Correct Answer:
The inverse of linear function is a function
Evaluate f(1) for f(x) = ln x.
Correct Answer:
0
What is the solution set to the equation log2(3x + 1) + log2(x + 7) = 5?
Correct Answer:
{1}
if you know ANY of these please let me know PLEASE PLEASE
You have to remember that the inverse of a logarithm is the exponential.
Q1: 210 = 1024
Should read 2^10 = 1024
Read in exponential general form in words....
2 raised to the tenth power equals 1024
Read in it's correct logarithmic form
Log base 2 of 1024 equals 10.
Do you see that all of the numbers are used in both equation, but in different places?
log 2 1024 = 10 That 2 should be smaller font and a subscript between the log and the 1024
Q2: 2log 4 + 3log 2
Addition with logs that have the same base can be condensed by mulitplying.
A number written in front of a logarithm is an exponent in condensed form.
log 4^2 + log 2^3 = log (4^2 * 2^3) = log 16 * 8 =
Log 128
Q3: Ted's comic book collection, which was worth $1300 five years ago, has been increasing in value by 12% per year since then. Which expression gives the current value of the collection?
1300(112%)(5 years)
I = Prt Interest = Principal * rate * time
Principal = $1300 initial amount the books were worth
rate = 12% + 100% (original value) = 112% or 1.12
time = 5 years
Q4:
The inverse of linear function is a function
What are your other choices? The inverse of a quadratic function is not a function. I can't think of a linear function whose inverse isn't a function. (You know to find the inverse, you switch out the variables x and y and solve for y again, right?)
Q5:
f(1) for f(x) = ln x
Remember that the base of that natural log is e.
Any number raised to the 0 power is 1 whether it is an e or an x or a 2. (2^0 = 1), (x^0 = 1)
Q6:
log2(3x + 1) + log2(x + 7) = 5
Condense your equation before you solve.
Log 2 (3x + 1)(x + 7) = 5
(3x + 1)(x + 7) = 3x^2 + 21x + x + 7 = 3x^2 + 22x + 7
log 2 3x^2 + 22x + 7 = 5
Write in exponential form
2^5 = 3x^2 + 22x + 7
32 = 3x^2 + 22x + 7
0 = 3x^2 + 22x - 25
Factor
(3x + 25)(x - 1) = 0
x = -25/3 x = 1
x = 1 is the only answer that can exist in a logarithm since all negative values do not.
i hope this helps!
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