logarithmic form question

Question

(a) Given 6^3=216, write an equivalent statement in logarithmic form.
(b) Given log_2?√8=3/2, write an equivalent statement in exponential form

Answer 1

log ₆ 216 = 3          216 = 6 ^3

 

log₂ √8 = 3/2           √8 = 2^ 3/2

Answer 2

a) in 6^3=216 the base is 6, the exponent is 3, and "the number" is 216.

the equivalent logarithmic form is log_6(216) = 3.

the two forms contain the same information: base 6, exponent/logarithm 3, number 216

 

b) log_2(sqrt(8))=3/2 written in exponential form is 2^(3/2) = sqrt(8)