Question 1005257
i think what you are saying is log of (1/27) to the base of (1/3) = x


in algebra.com that would be written as log(1/3,1/27) = x


in fact, place three opening brackets "{" in front and 3 closing brackets "}" in back and the statement log(1/3,1/27) = x looks like {{{log(1/3,1/27) = x}}}.


the general form is log(a,b) = c means log of b to the base of a = c


the basic definition of logs states:


log(a,b) = c if and only if a^c = b


using that basic definition and applying it to the case where a = 1/3, and b = 1/27 and c = x, you get:


log(1/3,1/27) = x if and only if (1/3)^x = (1/27)


this statement is true when the value of x = 3.


to confirm, replace x with the value of 3 in the equation log(1/3,1/27) = x, and you get:


log(1/3,1/27) = 3


this is true if and only if (1/3)^3 = (1/27).


evaluate this statement and you get 1/27 = 1/27 which is true.


this confirms the value of x = 3 is the solution to your problem.