Question 27408
 I was wondering if you could perhapse teach me how to solve this question step by step. thank you. 
Solve for b. 
logb(1/512)= -3

The definition of the logarithm of a non zero number N to a given base b 
is defined as the power p  to which the base b has to be raised to give 
the number N
That is logb(N) = p means b^p = N
Using this definition,
logb(1/512)= -3
gives b^(-3) = 1/512
That is 1/b^3 = 1/8^3  (using y^(-n) = 1/y^n )
which implies b^3 = 8^3
which gives b=8 (powers are equal and hence bases are equal)
Answer: b=8