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.

Algebra ->  Linear-equations -> 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.      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!

That's not what I got.

10%5E%282x-1%29+=+e%5E%284x-3%29

Let's take the natural log of both sides:

ln%2810%5E%282x-1%29%29+=+ln%28e%5E%284x-3%29%29

Use the rules of logarithms:

%282x-1%29ln%2810%29+=+4x-3

Let ln%2810%29=L for ease of writing:

%282x-1%29L+=+4x-3

Reverse the factors to make it more
like standard problems:

L%282x-1%29+=+4x-3

Distribute:

2Lx-L+=+4x-3

Get all and only x-terms on the left

2Lx-4x=L-3

Factor out x on the left:

x%282L-4%29=L-3

Divide both sides by %282L-4%29

x=%28L-3%29%2F%282L-4%29

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

x=-1.152427735

Edwin