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# A level maths C2 logs question watch

1. Any help solving this would be immensely appreciated x
2^(2x+3)= 3^(3x+2)
2. (Original post by Hardy jacks)
Any help solving this would be immensely appreciated x
2^(2x+3)= 3^(3x+2)
First start by taking logs of both sides so you get

How could you then simplify that?
3. (Original post by KaylaB)
First start by taking logs of both sides so you get

How could you then simplify that?

Well applying change of base straight away didn't work
4. (Original post by Hardy jacks)
Well applying change of base straight away didn't work
When there's a power after logging, you can bring it down to the left, then it's just algebra manipulation
5. Alternatively, you should get the same result by using
6. (Original post by Hardy jacks)
Well applying change of base straight away didn't work
Apologies, It's so useful that we just shorten it!
You could absolutely take logs with whatever base you like for these, it doesn't really matter.

In terms of simplifying
Are you familiar with this rule?

Even so, how could that rule be applied to the above so that we can simplify it and solve for x?
7. [QUOTE=RogerOxon;69638674]Alternatively, you should get the same result by using [/QUOTE
I'm sorry I'm really confused could anyone actually get -0.06... as their answer?
8. take log of both sides -> use log(a^b) = b x log(a) -> expand brackets -> rearrange for x
if you've done the manipulation correctly you'll get this:
x = log(9/8) / log(4/27)
9. (Original post by Hardy jacks)
I'm sorry I'm really confused could anyone actually get -0.06... as their answer?
Your answer (-0.0617 to 3 s.f.) looks correct - putting it into the original equation gives:

Here's my full working:

Take log of each side:

The other approach is:

Which is the same as above.

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