Exponent Definition and 220 Threads

Hey guys, It's been a while since I've even done simple exponent-based math. I'm trying to solve for x where 1.00062142^x = 4 I realize that this could also be written as the X root of 4 = 1.00062142 but this doesn't help me either because I don't know how to solve for it either way...

I need a little 'suggestion' as to how to integrate cos^6x sin^-3x dx. I rewrite to cos^6x/sin^3x dx and let u = sinx but when I'm trying to rewrite integral, what should I do with the ^6? Thanks!

Homework Statement express the given expression in simplest form with only possitive exponents Homework Equations **refer to attached drawing** The Attempt at a Solution Refer to attached drawing to see my attempt and to see what the real answer is. I don't understand where i...

Hi, I have the equation \sqrt{128} = 2^{m} I know that m is \frac{7}{2} as 2^7 = 128 from binary. However, say the equation was \sqrt{128} = 2^{m} how do I go about finding m. Can someone show me the technique Thankyou Tom

(A) Determine all possible values of R that yields multiple solutions to the equation: 2^P – 3^Q = R; where P, Q and R are all positive integers. (B) Determine all possible values of R that yields multiple solutions to the equation: 2^P – 3^Q = R; where P, Q are positive...

i know what the meaning of a^p is when p is an integer or rational. e.g., a^3 = a.a.a or a^{\frac{1}{5}} is such a number that when multiplied five times gives the number a. but what is the menaing of a^p when p is an irrational number?

Hi I am currently doing this problem and ran into a fork in the road- 6ab - 2b2 / 12ab - 4b2 I got .5ab + .5b2 as my answer. Now I am wondering if the second part is right because I am not sure if -2b2 / -4b2 is either .5b2 or just 1.. because the exponents 2-2= 0 and anything with...

Here's the problem: A metal is deformed in a tension test into its plastic region. The starting specimen had a gage length = 2.0 in and an area .50 sq. in. At one point in the tensile test, the gage length = 2.5 in and the corresponding engineering stress = 24000 psi; at another point in the...

Hi all, I've been trying to get back into mathematics by teaching myself calculus. I've been starting with the book "Calculus Made Easy" and have been doing fine except for one little thing I encountered on page 57. He shows a mathematical proof of why the derivative of y = x^\frac {1} {2}...

This problem was found in my gre test practice guide and i am having trouble understanding why the answer i chose was wrong. x^2 =16 y^3= 64 Which is bigger x or y? I chose that they were both equal to 4 however the answer stated that the relationship cannot be determined from the...

The book and lecture notes do not give a good example of how to solve this type of problem. After writing out f' I don't know how to simplify. Any hints? \begin{array}{l} f(x) = x - 5(x - 1)^{2/5} \\ \\ f'(x) = \frac{{f(x + h) - f(x)}}{h} = \frac{{(x + h) - 5((x + h) - 1)^{2/5} -...

Dear all, Does anyone know how to determine which of the following sum is larger? Thanks a lot! \sum_{i=1}^n a_i^{1/3}\sum_{i=1}^n a_i n\sum_{i=1}^n a_i^{4/3} a_i>0 \forall i This is two polynomial of the same order. It is not clear to determine which one is larger, if I...

Hi dudes, don't be put off by the clumsy notation here. I was wondering about these particular exponent towers and this curious property of theirs... Let p be a positive integer. Then the exponent tower, composed of p+1 parts each of value p^(1/p), equals p. e.g. for p=2. tower part...

How do you do this problem (without a calculator) that looks deceivingly simple, yet is utterly confusing. (2 ^ 30 - 2 ^ 29)/2 = ?. The answer is 2 ^ 28, but how was this done without using a calculator. The furthest I can take this without using a calculator is 2 ^ 29 - 2 ^ 28

1 = a^{b} How can I isolate b in that equation? Thanks. ^^

\sqrt x = x^ {.5} and \sqrt [.5] x = x^2 They are the same but i want to know why.

i solved ODE with Lagrange method and got stuck with integral \int x^2 e^{\frac{1}{2}x^2+x} dx i couldn't solve it with any method but combined and got the answer that it is \int x^2 e^{\frac{1}{2}x^2+x} dx=C+(x-1)e^{\frac{1}{2}x^2+x} the problem is that i want to do it with proper...

I know there's a formula somewhere, but how do you factor an equation with an exponent of three. In my solution's manual it says: x^3 - x^2 + 11x - 6 = (x-1)(x-2)(x-3) And I'm just trying to figure out how they got that. Thank you.

Infinite Exponent "towers" Please help me solve this problem; I don't even know how to start... Solve for x: x^{x^{x^{x^{...}}}}=2

how to convert an exponent to binary number?