SOLUTION: how do I solve this equation: (1/16) raised to power x equals 2 ???

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how do I solve this equation: (1/16) raised to power x equals 2 ???       Log On


   

Question 847703: how do I solve this equation: (1/16) raised to power x equals 2 ???
Found 2 solutions by swincher4391, Alan3354:
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
(1/16)^x = 2
log%28%281%2F16%29%5Ex%29+=+2
+x+%2A+log%281%2F16%29+=+log%282%29
+x+=+log%282%29+%2F+log%281%2F16%29
+x+=+-1%2F4

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how do I solve this equation: (1/16) raised to power x equals 2 ???
----------
%281%2F16%29%5Ex+=+2
The "hard way"
x*log(1/16) = log(2)
x = log(2)/log(1/16)
x = -0.25 = -1/4
=======================
If you spot that 1/16 = 2^-4, then
%282%5E-4%29%5Ex+=+2
2%5E%28-4x%29+=+2%5E1
-4x = 1
x = -1/4