Log question (HL maths)

polka dot

Okay so I wanted to do question 5 as a back up on Friday. What's everyone expecting to come up on it?

Also: How the heck do you do change of base law?

Here is my problem:

Show that log[base3](2-3x) = 2log[base9](2-3x)

PJelly

Bring the two over the second log so its squared.
Change the base on the right side so you get Log(3)[2-3x]^2 (all over) Log(3)[9]
which equals that previous log over two.

Multiply across by that two and on the left you get 2log[base3](2-3x) which is equal to Log(base3)[2-3x]^2
Which equals the right hand side.

polka dot

You are a life saviour! Thank you so much. I've spent the last half an hour trying to figure out how to do "log(3)9" on my calculator before I managed to get it by sheer dumb luck...

Question 5 is obviously going to go well.

Patriciamc93

polka dot wrote: »

Okay so I wanted to do question 5 as a back up on Friday. What's everyone expecting to come up on it?

Also: How the heck do you do change of base law?

Here is my problem:

Show that log[base3](2-3x) = 2log[base9](2-3x)

Don't forget page 21 of log tables. They really are a major help!

PJelly

Oh and this is how I remember change of base law
Log of the number (not the base) on top
Log of the base on the bottom of the fraction

Now set them both to any base

Like... (assume brackets means base) Log(2)3
Equals Log(anything)3 All over Log(anything, but must be same as above)2

And, lets assume we change to base 5, and / denotes a fraction.
Log(8)3 = Log(5)3/Log(5)8

Geddit?

PJelly

polka dot wrote: »

You are a life saviour! Thank you so much. I've spent the last half an hour trying to figure out how to do "log(3)9" on my calculator before I managed to get it by sheer dumb luck...

Question 5 is obviously going to go well.

Oh I just did it in my head. Just think, it's saying "What power do I put three to, to get nine?"
Answer is two. 3^2 is nine ^_^

polka dot

PJelly wrote: »

Oh I just did it in my head. Just think, it's saying "What power do I put three to, to get nine?"
Answer is two. 3^2 is nine ^_^

Everything makes so much more sense when you think of it that way. :rolleyes:

Is the question meant to be more binomial expansions this year or more logs/everything else?

Thank you everyone.

PJelly

polka dot wrote: »

Everything makes so much more sense when you think of it that way. :rolleyes:

Is the question meant to be more binomial expansions this year or more logs/everything else?

Thank you everyone.

I honestly have no idea.
Not including proofs, I think its basically impossible to predict a maths exam

conlufc

PJelly wrote: »

Oh and this is how I remember change of base law
Log of the number (not the base) on top
Log of the base on the bottom of the fraction

Now set them both to any base

Like... (assume brackets means base) Log(2)3
Equals Log(anything)3 All over Log(anything, but must be same as above)2

And, lets assume we change to base 5, and / denotes a fraction.
Log(8)3 = Log(5)3/Log(5)8

Geddit?

I understand it......just
Q5 isnt da worst...logs and proof by induction would b nice

polka dot

PJelly wrote: »

I honestly have no idea.
Not including proofs, I think its basically impossible to predict a maths exam

Are there proofs for this question?

PJelly

Yeah, a fraction with logs that ends in 1/log(r!)30