SOLUTION: 0.9872^X=0.5 how do i figure out what X is without just putting in numbers and seeing if they equal 0.5?

Algebra ->  Square-cubic-other-roots -> SOLUTION: 0.9872^X=0.5 how do i figure out what X is without just putting in numbers and seeing if they equal 0.5?      Log On


   

Question 33523: 0.9872^X=0.5
how do i figure out what X is without just putting in numbers and seeing if they equal 0.5?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+0.9872%5Ex+=+0.5+

Take logs: +log%280.9872%5Ex%29+=+log%280.5%29+
+xlog%280.9872%29+=+log%280.5%29+
+x+=+%28log%280.5%29%29%2F%28log%280.9872%29%29+
--> x = 53.80480576
--> x = 53.8048 to 4dp.

Check on your calculator: +0.9872%5E%2853.8048%29+ is 0.5000000 to 6 dp.

jon.