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Posted by **marcus** on Wednesday, November 21, 2012 at 3:05am.

5 In x=10?

log(x+25)=1+ log(2x-7)?

- precalculus -
**Kay**, Wednesday, November 21, 2012 at 4:51amYou have to know the logarithm rules and definition

Definition: if log(base a)x=b then x=a^b

Rules-I am going to use base 10 but it applies for every base:

1) loga^r=rloga

2)log(a*b)=loga+logb

3)log(a/b)=loga-logb

4)change of base: loga=log(base b)a/log(baseb)10

So the first one I don't understand question.

Second: lnx=2 so x=e^2 (by definition)

Third: log(x+25)-log(2x-7)=1 so by using 3rd law: log[(x+25)/(2x-7)]=1 and then definition; 10^1= (x+25)/(2x-7) so cross multiplying; 10(2x-7)=x+25 so 20x-70=x+25 19x=95 x=5

Hope this helps

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