SOLUTION: Find the value of log 16 to base 1/2

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Question 1186219: Find the value of log 16 to base 1/2


Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%281%2F2%29%2C16%29 = y
exponent equiv
%281%2F2%29%5Ey = 16
solve for y using natural logs
y*ln(1/2) = ln(16)
:
y = ln%2816%29%2Fln%281%2F2%29
y = -4 is the value
:
:
Check on calc: enter .5%5E-4 = 16

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


x=log%281%2F2%2C16%29

Put the equation in exponential form:

%281%2F2%29%5Ex=16

1/2 and 16 are both integer powers of 2, so you don't need to use logarithms to solve the equation.

%282%5E%28-1%29%29%5Ex=2%5E4
2%5E%28-x%29=2%5E4

The bases are the same, so the exponents are equal

-x=4
x=-4

ANSWER: log(1/2,16) = -4