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IB maths question

(4^x)+(2^[x+2]) = 3

I tried making it log4^x + log2^(x+2) = log3 etc etc etc but I’m so confused - it’s just giving the wrong answer. Is this the right step? It is on a logarithms paper... please help

Reply 1

OliverClarke

Edit : it’s 4^x + 2^(x+2) = 3 sorry typo!

Reply 2

tande33

Original post by OliverClarke

Edit : it’s 4^x + 2^(x+2) = 3 sorry typo!

The question is a disguised quadratic. If you make a substitution, you can solve the quadratic then use logs to find the answer.

Spoiler

If still stuck view spoiler, then if that doesn't help just say.

Reply 3

OliverClarke

Original post by tande33

The question is a disguised quadratic. If you make a substitution, you can solve the quadratic then use logs to find the answer.

Spoiler

If still stuck view spoiler, then if that doesn't help just say.

Thank you! That’s brilliant !

Just as a side question - would it be possible to make it into log4^x etc and solve from there? I don’t see why it wouldn’t be but I keep getting the wrong answer

Reply 4

tande33

Original post by OliverClarke

Thank you! That’s brilliant !

Just as a side question - would it be possible to make it into log4^x etc and solve from there? I don’t see why it wouldn’t be but I keep getting the wrong answer

no you can't (unfortunately!) as in the first step, you have to take the log of (4^x + 2^x+2) and you can't rearrange this to help you! Does that make sense? Think of it if you have x+y=1 , it doesn't mean that x^2+y^2=1 !

(edited 3 years ago)

Reply 5

OliverClarke

Original post by tande33

Got you! So you can only take the log when there is no addition?

Reply 6

tande33

Original post by OliverClarke

Got you! So you can only take the log when there is no addition?

There is nothing to stop you from taking the log of say x+3, but it won't help much as you won't be able to simplify it. So as a general rule isolate the unknown before taking logs.