1. ## Logarithims Help

Have a few questions that have to deal with logarithims. I dont quite understand them all and need some help. The first question is

1. Use what you know about polynomials to find the maximum value of the function. F(x)= 3+4x^2 - x^4 (Hint: set t=x^2)

2. Graph the polynomial without using a calculator ( i.e. find the zeros then use test points.)
P(x)= (1/8)(2x^4 +3x^3 - 16^2 - 24)^2

5. Find the following;
a. f(x) = ln(ln(ln x)
b. f(x) = log base 2(log base 10(x))

6. Use the change of base formula to show that
a. Log base 10 = (1/ln 10)

2. Originally Posted by Eandrews
Have a few questions that have to deal with logarithims. I dont quite understand them all and need some help. The first question is

1. Use what you know about polynomials to find the maximum value of the function. F(x)= 3+4x^2 - x^4 (Hint: set t=x^2)

Mr F says: The maximum value of F(x) is the same as the maximum value of G(t) = 3 + 4t - t^2. Do you know how to find the maximum value of a parabola?

[snip]

5. Find the following;
a. f(x) = ln(ln(ln x)
b. f(x) = log base 2(log base 10(x))

Mr F says: What are you meant to find ....?

6. Use the change of base formula to show that
a. Log base 10 = (1/ln 10) Mr F says: Log base 10 of what ....? Either the argument of the log is missing or the base is missing ....
This is all I have time for right now.

3. it doesnt say what to solve for in problem 5 my mistake for 6 its
log e=(1/ln10)

4. Originally Posted by Eandrews
it doesnt say what to solve for in problem 5 my mistake for 6 its
log e=(1/ln10)
This still makes no sense.

You mean $\log_{10} e$, right? (Which you could have written as log(base e) (10), for example).

Then note:

$x = \log_{10} e \Rightarrow 10^x = e \Rightarrow \ln 10^x = 1 \Rightarrow x \ln 10 = 1 \Rightarrow x = \frac{1}{\ln 10}$.

In other words, $\log_{10} e = \frac{1}{\ln 10}$.

5. Originally Posted by Eandrews
it doesnt say what to solve for in problem 5 [snip]
Then you need to get clarification from your instructor.