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logarithmic form 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

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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log 6 216 = 3          216 = 6 ^3
 
log2 √8 = 3/2           √8 = 2^ 3/2
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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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)