Precalc HELP, ASAP. No idea, Please explain

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Jul 2010
20
1
New Jersey
Solve leaving answers in terms of e or ln.

a) e^(5x-3)=10



b) 5^(3+x) = 20^x-3
 
Mar 2009
378
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\(\displaystyle \ln\) basically undoes \(\displaystyle e\). So if you want to isolate the exponent of \(\displaystyle e^x\) we can take the natural log like so \(\displaystyle \ln e^x = x\). Now don't forget whatever you do to one side of an equation you have to do to the other side of the equation. Also, don't forget that \(\displaystyle \ln a^x = x\cdot \ln a\). Make an attempt at these problems and post what you come up with.
 
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Jul 2010
20
1
New Jersey
alright thank you!

is this correct:

5x - 3 = ln 10

5x = ln 10 + 3

x = [(ln 10) + 3] / 5
 
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Jul 2010
20
1
New Jersey
thank you, and for the second one, im stuck here but i have

ln5 (3+x) = ln 20 (x-3)

3 ln5 + x ln5 = x ln20 - 3 ln20

3 ln5 + 3 ln20 = x(ln20 - ln5)
 
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