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Math Help - How do I solve this Exponential and Logarithmic Function?

  1. #1
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    How do I solve this Exponential and Logarithmic Function?

    1.Find the value of when = 4.

    My attempt:
    == 4
    =4
    27x=1
    x= 1/27.

    When checked on a calculator it doesn't work. I don't understand what to do. Is there a way to solve this without using calculators?

    2. Solve the equation

    I don't have an attempt since I can't understand what operation to use.

    Whoops, wrong category. Can I request for a Moderator (if there is one in here) to relocate this to Algebra?

    Now how do I mark this thread as [SOLVED]? There was a prefix box when I was just making this thread earlier.
    Last edited by RPSGCC733; October 14th 2012 at 01:51 AM.
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  2. #2
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    Re: How do I solve this Exponential and Logarithmic Function?(Sorry, wrong category)

    Quote Originally Posted by RPSGCC733 View Post
    1.Find the value of when = 4.

    My attempt:
    == 4
    =4
    27x=1
    x= 1/27.

    When checked on a calculator it doesn't work. I don't understand what to do. Is there a way to solve this without using calculators?

    2. Solve the equation

    I don't have an attempt since I can't understand what operation to use.

    Whoops, wrong category. Can I request for a Moderator (if there is one in here) to relocate this to Algebra?
    \displaystyle \begin{align*} 3^{9x} &= \left( 3^3 \right)^{3x} \\ &= 27^{3x} \\ &= \left( 27^x \right)^3 \\ &= 4^3 \\ &= 64  \end{align*}
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  3. #3
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    Re: How do I solve this Exponential and Logarithmic Function?(Sorry, wrong category)

    Quote Originally Posted by RPSGCC733 View Post
    1.Find the value of when = 4.

    My attempt:
    == 4
    =4
    27x=1
    x= 1/27.

    When checked on a calculator it doesn't work. I don't understand what to do. Is there a way to solve this without using calculators?

    2. Solve the equation

    I don't have an attempt since I can't understand what operation to use.

    Whoops, wrong category. Can I request for a Moderator (if there is one in here) to relocate this to Algebra?
    Is the second question trying to solve for \displaystyle \begin{align*} x \end{align*} when \displaystyle \begin{align*} \log_x{\left( \log_2{256} \right)} = 3 \end{align*}?
    Thanks from RPSGCC733
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  4. #4
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    Re: How do I solve this Exponential and Logarithmic Function?

    Note that
    (3^{9})^x = (3^{3\cdot 3})^x = 3^{3\cdot 3 \cdot x} = \ldots = ?

    \log_x(\log_2(256))=3 where \log_2(256)=8 thus you have to solve
    \log_x(8)=3 \Leftrightarrow x^3 = 8 \Leftrightarrow \ldots
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    Re: How do I solve this Exponential and Logarithmic Function?(Sorry, wrong category)

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*} 3^{9x} &= \left( 3^3 \right)^{3x} \\ &= 27^{3x} \\ &= \left( 27^x \right)^3 \\ &= 4^3 \\ &= 64  \end{align*}
    Ah. Thanks! Didn't think that 3^{9x} was 3^3 raised to the third power all along.

    Yeah, it was trying to solve for x.
    Last edited by RPSGCC733; October 14th 2012 at 01:26 AM.
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  6. #6
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    Re: How do I solve this Exponential and Logarithmic Function?

    1.) A similar approach to the one already posted:

    27^x=4

    3^{3x}=4

    3x=\log_3(4)

    9x=\log_3(64)

    3^{9x}=3^{\log_3(64)}=64
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  7. #7
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    Re: How do I solve this Exponential and Logarithmic Function?

    Quote Originally Posted by Siron View Post
    Note that
    (3^{9})^x = (3^{3\cdot 3})^x = 3^{3\cdot 3 \cdot x} = \ldots = ?

    \log_x(\log_2(256))=3 where \log_2(256)=8 thus you have to solve
    \log_x(8)=3 \Leftrightarrow x^3 = 8 \Leftrightarrow \ldots
    Many thanks.

    Isn't multiplication in Logarithm denoted with a + sign? That part confused me.
    Nevermind, I just realized it wasn't multiplication. \log_2(256)=8 was a logarithm of \log_x(y)=8
    Last edited by RPSGCC733; October 14th 2012 at 01:42 AM.
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  8. #8
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    Re: Exponential and Logarithmic Function?(Sorry, wrong category)

    Hello, RPSGCC733!

    \text{2. Solve: }\:\log_x\left[\log_2(256)\right] \:=\:3

    \begin{array}{ccc}\text{Given:} & \log_x\left[\log_2(256)\right] \:=\:3 \\ \\ \text{Then:} & x^3 \:=\:\log_2(256) \\ \\ & x^3 \:=\:\log_2(2^8) \\ \\ & x^3 \:=\:8 \\ \\ & x \:=\:2 \end{array}
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