Question 950304
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.