# exponents

1. ### Logarithmic word problem

Hi, I hope someone can help me with the following question: Can someone please let me know whether my solution is correct? I said that in about in year 2015, the amount pests would be the same. The reason why I want to know whether I'm right is because my solution does not match up to the...
2. ### Solve exponential equation

Hi, I'm currently trying to solve for the following exponential equation: 3^(2x)-5(3^x)=-6 I'm hoping that someone can explain why the steps I took to solve this equation are incorrect: line 1 - 3^(2x)-5(3^x)=-6 line 2 - 3^(2x)-15^x=-6 line 3 - 3^x(1^x-5) = -6 line 4 - 3^x(-4)=-6 line 5 -...
3. ### Exponential equation word problems

Hi, I hope someone can help. I'm trying to solve the following question: As stated above, the equation is N(t) = 3^(t+1). N(t) represents the number of people told during the hour t, and t = 1. However, let's say that we wanted to develop an equation which fit the same context that...
4. ### Simplifying exponential expression

Hi, So I have the exponential expression (16x^6)^(1/2). I got the solution 4x^2, which I thought was correct. However, according to my textbook, the solution is 4|x|^2. Do anyone know why this is so? I hope someone can help!
5. ### Exponents as Coefficients

Can an exponent ever be considered the coefficient of a variable? For instance, in the expression x^2, what is the coefficient of x? Is it 2, or is it x, since x^2 = x*x?
6. ### Equating two equations - basic algebra questions re exponents and trig functions

Hi, I have the following: Consider the following two expressions: f(x) = e ^(2x) − (e^(x) cos x)^ (2)/x^2 and g(x) =  (e^xsin x/x)^2 I have to show that these equations are equal for x not equal to 0. I have a couple of basic questions: When an expression is expressed to the power 2...

$\left[\left(\frac{B\cdot 3^{\frac{1}{\left(x-1\right)}}}{1+3^{\frac{1}{\left(x-1\right)}}}\right)^x+3\left(\frac{B}{1+3^{\frac{1}{\left(x-1\right)}}}\right)^x\right]^{\frac{1}{x}}$ This is as far as I can get...
8. ### Bases, Exponents, and Digits

Question: What's the smallest positive value of k such that the base nine representation of $\left ( 27_{ten} \right )^{k}$ has exactly 9999 (base ten) digits? Work thus far: I know that in base ten to find the number of digits you just take the common log and round up, and I'm guessing that...

I am looking at two different methods of solving one simple problem, that give conflicting answers, and would like to know which of my solutions is wrong. The problem is simple: simplify the square root of a square. Example: (x2)(1/2) Here are steps that prove the answer is x: (x2)(1/2) =...
10. ### Polynomials with fractional exponents

I have to solve for x in each of these equations. Help would be appreciated. (x^2/5)+(3x^1/5)+2=0 I tried increasing both sides to the 5th power to solve this, but I came up with some answers that I don't think are correct. (x^1/2)-(13x^1/4)+36=0 My only idea for solving this one is to...
11. ### Rearranging Equations with Exponents

Hi, I've always considered myself fairly good with maths however it's been a few years and I'm obviously rusty. I have an equation with an exponent that I would like to rearrange, however the placing of the exponent on the other side is confusing me. The equation (fairly simple) is as follows...
12. ### Exponential/Natural Log and Fractional Exponents

Hello, I would like help solving for x in this problem: Y = (exp[3x^2] - 3 exp[x^2] +2)/((exp[x^2] -1)^(3/2)) Where Y= 0.5755 The Y and X are just actually gamma and theta, but I just used Y and X as placeholders. This is an equation from a 1967 streamflow modeling paper. I know that I can...
13. ### Implicit Differentiation (Issue with exponents)

It deals with implicit differentiation. I am having trouble understanding the final part of the problem dealing with exponents. I was asked to find \frac{d^2y}{dx^2} for x^4 + y^4 = 16. My work: 4x^3 + 4y^3 \cdot \frac{dy}{dx} = 0 4y^3 \cdot \frac{dy}{dx} = -4x^3 \frac{dy}{dx} =...
14. ### Proof for Rational Exponents

Hi everyone, So I've been using rational exponents for a while now, and I began to wonder why do they work in a similar way to integer exponents? Like if you have f(x) = x0.25 if you multiply it my itself 4 times you just get x? Thanks in advance :)
15. ### Rational roots

Hey guys! I'm in pre calculus not sure if this is the right forum but my problem says "list the possible rational roots of the equation. Then determine the rational roots" and the equation is x(to the 3rd) + 2x(to the 2nd) -6x +3=0 been working on it for an hour and am lost. Appreciate the help...
16. ### Help with problem

Hey guys my names Joey I'm new and there is something that I'm stuck on in math. How do I find the roots of the equation t(to the 3rd power) + 2t(to the 2nd power) – 4t – 8=0
17. ### Factoring Out Negative Exponents

http://imgur.com/G1hNHou I've eliminated answer choices B, C, and D, and I'm pretty sure the answer is A. I'm not sure if I've mixed up a sign or something, because I keep getting answer choice A but with 1 instead of 1+2x in the numerator. Help Please! Thank you
18. ### Factoring with negative exponents

Could some one explain how to factor this trinomial into the factored form shown, thanks a lot. Link below is the equation Gyazo - 94e4038a9f1f30f4ff938b2849f58d15.png
19. ### decimal exponents

HI; Just need to know how to tackle expressions like this 3^1.2 what I did was 3^(12/10) = 3^(6/5) = 5root3^6. Thanks.
20. ### Exponents

I am having an issue with solving these. The first one I solved by multiplying the 2 that is outside the parentheses to the 3 inside of the parentheses to get 6. Then, I multiplied that 6 by the exponent of 2 next to the X inside of the parentheses and end up with (18x^2)^3. Lastly, I took the 3...