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C2 - Help with exponential equations please! watch

1. Hey mighty TSR math forum

I need to retake C2 soon. My logs are sluggish right now, i need to change that! here is the question (Btw I have the laws in my head, i just need a push in the right direction):

Solve 5^(2x) - 12[5^x] + 35 = 0

I get mixed up with these. I can do the simple logs fine!

Thanks!
2. If I rewrite 5^(2x) as , does that help?

Further hint (only open once you've thought about it):

Spoiler:
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Spoiler:
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Let u = 5^x
3. 5^2x = 5^x x 5^x

4. right. I got it!!

I did try (5^x)^2 before.

Now i see it!

you eventually get (x-5)(x-7)

I feel less of a crazy scientist now

Is there a rule with these though? Say there wasnt a 5^(2x) but say a 4^(2x) how would you use logs to solve a ******* like this?
5. (Original post by yurihammo)
Is there a rule with these though? Say there wasnt a 5^(2x) but say a 4^(2x) how would you use logs to solve a ******* like this?
In the 4^(2x) case, it's just (4^x)^2...

And no, you don't get (x-5)(x-7) = 0, you get (u - 5)(u - 7) = 0, which you then need to solve for u and THEN solve for x.

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Updated: September 26, 2010
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