SOLUTION: What is the best solution for 2.3^x = 48

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: What is the best solution for 2.3^x = 48      Log On


   

Question 23360: What is the best solution for 2.3^x = 48
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Do you know about logarithms? That is the best way! Take the ln of both sides:
2.3%5Ex+=+48
ln%282.3%5Ex%29+=+ln%2848%29

Use the property of logarithms that says log+M%5EN+=+N+log+M+
ln%282.3%5Ex%29+=+ln%2848%29
x%2A+ln%282.3%29+=+ln%2848%29

Now divide both sides of the equation by ln(2.3):
x%2A+ln%282.3%29+=+ln%2848%29
%28x%2A+ln%282.3%29%29%2F%28ln2.3%29+=+ln%2848%29%2F%28ln2.3%29

With a calculator, this is
x= 4.647807191 (approximately) which rounds off to 4.65.

If you would like to check this (and I would before I embarrass myself to the world by posting another wrong answer!!), you can use a calculator to calculate 2.3%5E%284.6478%29. Using the calculator value of x, it comes out to 48, so it checks!!

R^2 at SCC