Answer:
x = 1
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
Note that 9 = 3² and 27 = 3³ , thus
[tex]9^{x-2}[/tex] × [tex]27^{x}[/tex]
= [tex](3^2)^{x-2}[/tex] × [tex](3^3)^{x}[/tex]
= [tex]3^{2x-4}[/tex] × [tex]3^{3x}[/tex]
= [tex]3^{(2x-4+3x)}[/tex]
= [tex]3^{5x-4}[/tex] , then
[tex]3^{5x-4}[/tex] = [tex]3^{1}[/tex]
Since the bases on both sides are equal, equate the exponents
5x - 4 = 1 ( add 4 to both sides )
5x = 5 ( divide both sides by 5 )
x = 1
