Question

Solve the following logarithmic equation. log Subscript 3 Baseline left parenthesis x cubed minus 18 right parenthesis equals 2 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is StartSet nothing EndSet . ​(Type an exact​ answer.) B. The solution set is the set of real numbers. C. The solution set is the empty set.

Answer 1

Given :  log (base 3) x³ - 18  =  2    $log_{3}(x^3 - 18) = 2$

To find :  x

Solution:

$log_{3}(x^3 - 18) = 2$

=> 3² = x³ - 18

=> 9  = x³ - 18

=> 27 = x³

=> x = ∛27

=> x = 3

Solution set is unique   x =  3

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