Question

Use the definition of the logarithmic function to find x. log4 0.25=x x=?

Answer 1

\[\log_{4} \] 0.25=x x=?

Answer 2

change of base formula

--> log(.25)/log(4) = -1

Answer 3

wait i guess they want you to change .25 to 4^-1

Answer 4

\[\log_{4} 0.25=\log_{4}(1/4)=\log_{4}(4^{-1})=-1\]since the log function asks the question to what power of the base (in this case four) do I have to go to get the argument of the function (in this case 4^-1). Clearly, we raise four to the -1 power to get 4^-1.

Answer 5

The key to doing this problem without needing a calculator is the insight that 0.25=1/4.