Question 950304: what is the equation in logarithmic form for 16=(1/4)-2?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe you mean 16 = (1/4)^(-2)
if you use your calculator to evaluate this equation, you will see that:
16 = 16.
this confirms the equation is true.
the ^ symbol indicates exponentiation.
the equation is 16 = (1/4)^-2
this is in the form of y = b^x, where:
y = 16
b = (1/4)
x = -2
in general, y = b^x if and only if log(b,y) = x
log(b,y) means log of y to the base of b.
apply that to your problem and you get:
16 = (1/4)^-2 if and only if log(1/4,16) = -2
how do you confirm?
use your calculator and the log conversion formula that tells you that:
log(1/4,16) = log(16) / log(1/4).
remember that log without mention of the base means the base is 10.
log(16) / log(1/4) means log of 16 to the base of 10 divided by log of 1/4 to the base of 10.
log to the base of 10 is the LOG function in your calculator.
your equation becomes:
log(16) / log(1/4) = -2
use your calculator to get:
-2 = -2
this confirms the conversion is correct.
|
|
|
