SOLUTION: 10^(2x-1) = e^(4x-3) I'm just checking my answer it seems a bit strange. I got 0.1 for this problem.

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Question 172156This question is from textbook
: 10^(2x-1) = e^(4x-3) I'm just checking my answer it seems a bit strange. I got 0.1 for this problem. This question is from textbook

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
10^(2x-1) = e^(4x-3)
Take the log of both sides to get:
2x-1 = (4x-3)log(e)
-------
Recall: e = 2.71828...
-------
2x-1 = (4x-3)*0.43429...
2x-1 = 1.73718x - 1.3029
0.2628x = 0.3029
x = 1.1525...
==================
Cheers,
Stan H.
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!

That's not what I got.



Let's take the natural log of both sides:



Use the rules of logarithms:



Let  for ease of writing:



Reverse the factors to make it more
like standard problems:



Distribute:



Get all and only x-terms on the left



Factor out x on the left:



Divide both sides by 



Calculate  which equals ln(10)
or 2.302585093, plug that in for L and get



Edwin
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