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Thread: Indices & Logarithm: If u = log_4(x), show that log_x(4) = 1/u. Hence,...

  1. #1

    Indices & Logarithm: If u = log_4(x), show that log_x(4) = 1/u. Hence,...

    I can stuck on this question and unable to do it.



    If u = log4(x), show that logx(4) = 1/u. Hence, find values of x for which:

    . . . . .2 log4(x) + 3logx(4) = 7




    Can someone help me please?
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    Last edited by stapel; 06-21-2017 at 02:29 PM. Reason: Typing out the text in the graphic; creating useful subject line.

  2. #2
    Elite Member mmm4444bot's Avatar
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    What have you tried or thought about, so far?

    The first part of this exercise can be started with the Change of Base Formula or by switching to exponential form, and then thinking about the definitions of rational exponents. Maybe they're trying to demonstrate the relationship:

    base^exponent = power

    power^(1/exponent) = base

    For example:

    3^5 = 243

    243^(1/5) = 3

    For the second part, start by thinking about the first few powers of four, and for each power write out the values of the log expressions from the first part. Then check: Do any of these values satisfy the equation?
    Last edited by mmm4444bot; 06-18-2017 at 09:05 PM. Reason: Typo
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  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by Jx Chen View Post
    I can stuck on this question and unable to do it.



    If u = log4(x), show that logx(4) = 1/u. Hence, find values of x for which:

    . . . . .2 log4(x) + 3logx(4) = 7




    Can someone help me please?
    What are your thought? What have you tried? Where are you stuck?

    For instance, you started by converting the given log equation into its corresponding exponential equation:

    . . . . .u = log_4(x)

    . . . . .4^u = x

    Then you took the base-x log of either side, applied the relevant log rule, divided through by the u, and... then what?

    Please be complete. Thank you!

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