Results 1 to 8 of 8

Thread: Logarithms & Differentiations help please

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    9
    Awards
    1

    Logarithms & Differentiations help please

    This is my first time on these forums tell me if im doing anything wrong! , thanks

    First the Logarithms( Just learnt the latex functions lol had to read it before I posted)

    Use the laws of logarithms to solve the following indicial equations:

    (in each case check your answer by subtituting back the value for x)

    5^(x+2)=8.5


    6.5^x =8.4^(4x-10)

    now for the Differential and integral calculus

    Differentiate the following functions.

    y=4x^3 -2x^2 + 5x^-3.7-6 w.r.t. x

    s=4e^3t -e^-2.5t w.r.t. t

    y=4sin2\theta-3cos4\theta w.r.t. \theta


    Integrate the following expressions.

    \int(2x^3-3x^2+5x-2)dx


    \int (5sin2\theta+2cos4\theta)d\theta


    This work has to be in by monday morning, im missing these questions and I have tons of other college work to get on with
    Last edited by Problem_Solver11; Jun 28th 2008 at 01:20 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Problem_Solver11 View Post
    This is my first time on these forums tell me if im doing anything wrong! , thanks

    First the Logarithms( Just learnt the latex functions lol had to read it before I posted)

    Use the laws of logarithms to solve the following indicial equations:

    (in each case check your answer by subtituting back the value for x)

    5^(x+2)=8.5


    6.5^x =8.4^(4x-10)

    now for the Differential and integral calculus

    Differentiate the following functions.

    y=4x^3 -2x^2 + 5x^-3.7-6 w.r.t. x

    s=4e^3t -e^-2.5t w.r.t. t

    y=4sin2\theta-3cos4\theta w.r.t. \theta


    Integrate the following expressions.

    \int(2x^3-3x^2+5x-2)dx


    \int(5sin2\theta+2cos4\theta)d\theta


    This work has to be in by monday morning, im missing these questions and I have tons of other college work to get on with,I will give the first person with all the answers and working out 20 pound through paypal to thank them, thanks alot.
    For the first one take the natrual log of both sides. Then yank the exponent out as a coefficient and then solve for x.

    For the differentiation ones

    $\displaystyle \frac{d}{dx}\bigg[ax^n+bx^{n-1}+cx^{n-2}+\cdots\bigg]=\frac{d}{dx}\bigg[ax^n\bigg]+\frac{d}{dx}\bigg[bx^{n-1}\bigg]+\frac{d}{dx}\bigg[cx^{n-2}\bigg]+\cdots$

    $\displaystyle \frac{d}{dx}\bigg[ax^n\bigg]=nax^{n-1}$



    As for the other integrals, the concept of splitting works for integrals as well,

    and finally

    $\displaystyle \int{x^n}dx=\frac{x^{n+1}}{n+1}$

    And $\displaystyle \int\sin(n\theta)d\theta=\frac{-\cos(n\theta)}{n}$

    and

    $\displaystyle \int\cos(n\theta)d\theta=\frac{\sin(n\theta)}{n}$

    And don't forget $\displaystyle +C$, where $\displaystyle C$ is an abritrary constant of integration
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Thanks
    1
    I'm giving 30 pounds through paypal to people who don't do his homework for money.

    Do you know that if $\displaystyle a^b = c$, then $\displaystyle b = \log_a c$ for values of $\displaystyle a,c>0~~~a\neq 1$?

    Come on, I know you can do these if you want.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2008
    Posts
    9
    Awards
    1
    Quote Originally Posted by wingless View Post
    I'm giving 30 pounds through paypal to people who don't do his homework for money.

    Do you know that if $\displaystyle a^b = c$, then $\displaystyle b = \log_a c$ for values of $\displaystyle a,c>0~~~a\neq 1$?

    Come on, I know you can do these if you want.
    tamam ya habibi, btw mathstud are those the answers then :x?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Problem_Solver11 View Post
    tamam ya habibi, btw mathstud are those the answers then :x?
    Not answers, tools to reach the answer. That is what you should truly be seeking.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2008
    Posts
    9
    Awards
    1
    Quote Originally Posted by Mathstud28 View Post
    Not answers, tools to reach the answer. That is what you should truly be seeking.
    I really need the answers man it has to be in by monday otheriwise I might fail, i'm doing electronics engineering course and have to hand in alot on monday, but my teacher recently handed back my maths work and said 3 question were wrong and we did that ages ago and i've forgot how to do it, well to be honest I don't have time to do it, I would appreciate it alot.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    Post

    Quote Originally Posted by Problem_Solver11 View Post
    I really need the answers man it has to be in by monday otheriwise I might fail, i'm doing electronics engineering course and have to hand in alot on monday, but my teacher recently handed back my maths work and said 3 question were wrong and we did that ages ago and i've forgot how to do it, well to be honest I don't have time to do it, I would appreciate it alot.
    I will do the first one

    $\displaystyle 5^{x+2}=8.5$

    Taking the natural logs of both sides gives

    $\displaystyle (x+2)\ln(5)=\ln(8.5)\Rightarrow{x=\frac{\ln(8.5)}{ \ln(5)}-2}$

    I will also do one of each of the others

    $\displaystyle \frac{d}{dx}\bigg[4x^3-2x^2+5x^{-3.7}-6\bigg]=12x^2-4x-18.5x^{-4.7}$

    and

    $\displaystyle \int\bigg[5\sin(2\theta)+2\cos(4\theta)\bigg]d\theta=\frac{-5}{2}\cos(2\theta)+\frac{1}{2}\sin(4\theta)+C$
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jun 2008
    Posts
    9
    Awards
    1
    Quote Originally Posted by Mathstud28 View Post
    I will do the first one

    $\displaystyle 5^{x+2}=8.5$

    Taking the natural logs of both sides gives

    $\displaystyle (x+2)\ln(5)=\ln(8.5)\Rightarrow{x=\frac{\ln(8.5)}{ \ln(5)}-2}$
    funny enough I have that one already I put it up to see if I was right, Thanks though
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. applications of differentiations
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Jun 4th 2011, 06:15 AM
  2. Replies: 3
    Last Post: Jun 7th 2010, 02:43 PM
  3. Logarithms help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Mar 16th 2010, 04:30 AM
  4. Logarithms. Please help.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: Feb 25th 2010, 04:21 AM
  5. Implicit Differentiations
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Sep 30th 2008, 05:45 AM

Search Tags


/mathhelpforum @mathhelpforum