SOLUTION: I was wondering if you could perhapse teach me how to solve this question step by step. thank you. Solve for x. 10^(x-3)= e^(2x+5)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I was wondering if you could perhapse teach me how to solve this question step by step. thank you. Solve for x. 10^(x-3)= e^(2x+5)      Log On


   

Question 27417: I was wondering if you could perhapse teach me how to solve this question step by step. thank you.
Solve for x.
10^(x-3)= e^(2x+5)
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
This problem can be solved using natural logarithms. We need to use two properties of natural logarithms (ln):
ln%28a%5Ex%29=x%2Aln%28a%29 and
ln%28e%5Ex%29=x
We have:
10%5E%28x-3%29=+e%5E%282x%2B5%29
Now take the natural logarithm of both sides:
ln%2810%5E%28x-3%29%29=+ln%28e%5E%282x%2B5%29%29
Using the properties Imentioned before, we get:
%28x-3%29ln%2810%29+=+2x%2B5
This equation can now be easily solved
x%2Aln%2810%29+-+3ln%2810%29+=+2x%2B5
x%2A%28ln%2810%29+-+2%29+=+5%2B3ln%2810%29
x+=+%285%2B3ln%2810%29%29%2F%28ln%2810%29+-+2%29
x = 39.35...