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# Stuck on some natural log questions? watch

1. 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!
2. 1) First of all how would you draw the graph for ? Then how would you draw the graph of ?

2) First, spot that , is just . Now from the rule , we can sub into the , to get that . Now you can differentiate as normal using the chain rule.

3) First multiply out all the minus signs, then use the log rule .
3. (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 for both of the logs then combine the logs.
4. (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 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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Updated: January 3, 2015
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