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AQA Core 2 Logarithms Question

Hello,

I'm hoping someone can help me, I'm stuck on Q10(f) from Chapter 8 (Exponentials and Logarithms) of the book "Core 2 for AQA" by Cambridge The School Mathematics Project.

10. Solve these equations for x:

(f) 6^x-4 = 2^x+3

I've done all the other 1 - 14Qs in this exercise, I don't know why I'm struggling with this question so much (though I have been out of education for 4 years so I'm a little rusty!).

Any help would really be appreciated :smile:

Thanks

Reply 1

SamKeene

I would take the natural logs of both side:

ln(6^{(x-4)})=ln(2^{(x+3)})

(x-4)ln(6)=(x+3)ln(2)

Since ln(6) and ln(2) are constants, this is a linear equation in x in the form ax+b.

Rearrange to find x.

Reply 2

Muttley79

What have you tried?

Hint: the chapter is about logs ... how could they help?

SamK - we aren't supposed to post solutions, just hints!

Reply 3

alyyspp

Original post by SamKeene

I would take the natural logs of both side:

ln(6^{(x-4)})=ln(2^{(x+3)})

(x-4)ln(6)=(x+3)ln(2)

Since ln(6) and ln(2) are constants, this is a linear equation in x in the form ax+b.

Rearrange to find x.

Thank you so much :smile:

, I made things way too complicated for myself and had gotten in a complete mess.

Reply 4

alyyspp

Original post by Muttley79

What have you tried?

Hint: the chapter is about logs ... how could they help?

SamK - we aren't supposed to post solutions, just hints!

Oh I know the chapter is about logs, I have completed all the other 13 questions in the exercise, I was just having troubles rearranging this one.

Reply 5

SamKeene

Original post by alyyspp

Thank you so much :smile:

, I made things way too complicated for myself and had gotten in a complete mess.

For extra understanding, you might want to do the question without using the natural log. Take log base 6 on the left side, and log base 2 on the right side, then use the log law to change the base of one to be the same as the other, and solve that.