SOLUTION: How do you solve something like this: 2x=64 (2 to the x power equals 64) using logarithms other examples are 2 to the x power equals 100 10 to the x power equals 12 3 to

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do you solve something like this: 2x=64 (2 to the x power equals 64) using logarithms other examples are 2 to the x power equals 100 10 to the x power equals 12 3 to       Log On


   



Question 459917: How do you solve something like this:
2x=64
(2 to the x power equals 64)
using logarithms
other examples are
2 to the x power equals 100
10 to the x power equals 12
3 to the x power equals 48

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Ex=64
take log base 2 of both sides
log%282%2C2%5Ex%29+=+log%282%2C64%29
log%282%2C2%5Ex%29+=+log%282%2C2%5E6%29
x+=+6
.
2 to the x power equals 100
2%5Ex+=+100
log%282%2C2%5Ex%29+=+log%282%2C100%29
x+=+log%282%2C100%29
apply "change of base":
x+=+log%28100%29%2Flog%282%29
x+=+6.644
.
10 to the x power equals 12
10%5Ex+=+12
x+=+log%2812%29
x+=+1.079
.
3 to the x power equals 48
3%5Ex+=+48
x+=+log%283%2C48%29
x+=+log%2848%29%2Flog%283%29
x+=+3.524