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    I'm revising and I just have no idea how to do these questions. explainations would be much appreciated x

    1) Draw the graph of lnl2x-3l - its a modulus

    2) What is the derivitive of (1/2)^x

    3) what is (-4ln4)-(-4ln0.5)

    Thank you!
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    1) First of all how would you draw the graph for f(|x|)? Then how would you draw the graph of f(2x - 3)?

    2) First, spot that \left(\dfrac{1}{2}\right)^x, is just 2^{-x}. Now from the rule e^{\ln(a)} = a, we can sub 2^{-x} into the a, to get that 2^{-x} = e^{-x\ln2}. Now you can differentiate as normal using the chain rule.

    3) First multiply out all the minus signs, then use the log rule \ln(a) + \ln(b) = \ln(ab).
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    (Original post by JustHoping)
    I'm revising and I just have no idea how to do these questions. explainations would be much appreciated x

    1) Draw the graph of lnl2x-3l - its a modulus

    2) What is the derivitive of (1/2)^x

    3) what is (-4ln4)-(-4ln0.5)

    Thank you!
    1) Break up the graph into a combination of transformations starting with f(x) = ln(x)

    ln(x) -> ln|x| -> ln|2x| -> ln |2(x-1.5)|

    Each of these steps are graph transformations that you should be familiar with


    2) Write y = (1/2)^x then try taking logs of both sides. Next use implicit differentiation to find dy/dx. This is one of a few ways to tackle this.


    3) Use b\ln a = \ln a^b for both of the logs then combine the logs.
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    (Original post by notnek)
    1) Break up the graph into a combination of transformations starting with f(x) = ln(x)

    ln(x) -> ln|x| -> ln|2x| -> ln |2(x-1.5)|

    Each of these steps are graph transformations that you should be familiar with


    2) Write y = (1/2)^x then try taking logs of both sides. Next use implicit differentiation to find dy/dx. This is one of a few ways to tackle this.


    3) Use b\ln a = \ln a^b for both of the logs then combine the logs.
    Thank you, you've both been a big help. But I'm still a little confused about the last question?
 
 
 
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