Solve. 90^x = 27. Explain every step.

Answer:The answer is ⇒ x = 0.73244Step-by-step explanation:∵ 90^x = 27 ⇒ insert log in both sides∴ [tex]log(90)^{x}=log(27)[/tex]∵ 90 = 9 × 10 , 27 = 3³∵ log(a)^b = b log(a)∴ log(9 × 10)^x = x log(9 × 10)∴ [tex]xlog(9*10)=log(3^{3})[/tex]∵ log(a × b) = log(a) + log(b)⇒log(9 × 10) = log(9) + log(10)∴ [tex]x[log(9)+log(10)]=3log(3)[/tex]∵ log(10) = 1 , 9 = 3²∴ [tex]x[log(3)^{2}+1]=3log(3)[/tex]∴ [tex]x[2log(3)+1] = 3log(3)[/tex] ∴ x = (3log3)/[2log(3)+1]∴ x = 0.73244