Stuck on some natural log questions?

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!

Reply 1

0x2a

2

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)

.

Reply 2

Notnek

21

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.

Reply 3

JustHoping

OP

11

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?

Stuck on some natural log questions?

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