Each of the following can be rewritten in the form logA B C

Each of the following can be rewritten in the form log_A B = C. Give the values of A, B, and C for each of the equations below. 5^3 = 125 4^-3 = 1/64 p^m = k

Solution

exponential to logarithmic form :y = log_bx is equivalent to b^y = x.

a) 5^3 = 125

expoential to logarithmic form :y = log_bx is equivalent to b^y = x.

5^3 = 125 ----> 3 = log₅(125)

logA(B) = C: A = 5 , B = 125 , C=3

b) 4^-3 = 1/64

In logarithmic form : -3 = log₄(1/64)

logA(B) = C: A = 4 , B = 1/64 , C=-3

c) p^m =k

In logarithmic form : m = log_p(k)

logA(B) = C: A = p , B = k , C=m

d) 4^x = 5-y

In logarithmic form : x= log₄(5-y)

logA(B) = C: A = 4 , B = 5-y , C=x