If ₃ x¹⁶ +9 ₂₇ [3] 3 x =5 then x= .

Step-by-step solution

Simplify the equation ₃ x¹⁶ + 9 ₂₇ [3] 3 x = 5 using logarithmic properties. Apply the power rule to the first term: ₃ x¹⁶ = 16 ₃ x , so ₃ x¹⁶ = 4 ₃ x . Transform the base and argument in the second term: ₂₇ [3] 3 x = _ 3^3 ( 3 x )^ 1/3 = 1 3 ₃ ( 3 x )^ 1/3 = 1 9 ₃ ( 3 x ) Apply the quotient rule: 1 9 ( ₃ 3 - ₃ x) = 1 9 (1 - ₃ x) Thus, 9 ₂₇ [3] 3 x = 1 - ₃ x . The equation becomes 4 ₃ x + 1 - ₃ x = 5 , requiring ₃ x 0 for the square root to be defined. Let y = ₃ x with y 0 , so ₃ x = y^2 . Substituting yields 4y +