SOLUTION: solve the equation 3^x=500

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve the equation 3^x=500      Log On


   

Question 36554: solve the equation
3^x=500
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
3^x=500

Take the ln of each side:
+ln%283%5Ex%29+=+ln+%28500%29+

By law of logarithms:
+x%2A+ln%283%29+=+ln+%28500%29+

Now, just divide both sides by ln(3):
x+=+%28ln+%28500%29%29%2F%28ln%283%29%29+

By calculator, the answer is approximately 5.65678 or probably round off to 5.66.
R^2 at SCC