18^x-9^x=3^x(6^x-3^x); (6^x-3^x) cancels with itself, because exactly the same expression is in the denominator; or 6^x-3^x=t 18^x-9^x/t 18^x-9^x=3^x(6^x-3^x) 3^x * t / t = 3^x =3; x=1
(18^x - 9^x) / (6^x - 3^x) = 3 ------------------------------------------------------------------------------------------------------- 9^x(2^x - 1) / 3^x(2^x-1)) factor out 9^x on top and 3^x on bot 9^x / 3^x cancel out (2^x-1)/(2^x-1)) = 1 (9/3)^x property: a^x/b^x -> (a/b)^x 3^x = 3 9/3 = 3 x = 1 property: a^b = a -> a=1 done in 1 minute with no music
I'm sorry but there is NO WAY that this is a math Olympiad question !!! I solved it using basic algebra rules in about 23 seconds... CLICKBAIT NONSENSE>>>!
Math Olympiad exam is conducted for every grade of students. So, this is actually a math olympiad problem. This channel is dedicated to math olympiads for grade 10 or lower. On my second channel math booster, i cover math olympiad problems for grade 12 students.
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It is unnecessarily made complicated. This question doesn’t need to write down. You got 3^x=3 by taking 3*6=18 and 3*3=9.
18^x-9^x=3^x(6^x-3^x); (6^x-3^x) cancels with itself, because exactly the same expression is in the denominator; or 6^x-3^x=t
18^x-9^x/t
18^x-9^x=3^x(6^x-3^x)
3^x * t / t = 3^x =3; x=1
X = 1.
Doesn't seem hard. Did it in my head. 😊
9^x(2^x-1)=3*3^x(2^x-1) , 9^x=3*3^x , 3^2x=3*3^x , -> 3^x=3 , 3=3^1 , x=1 , test , x=1 , (18-9)/(6-3)=9/3 , 9/3=3 , same , OK ,
Isn't this a one-liner? 18^x - 9^x = (3^x) (6^x - 3^x); cancel (6^x - 3^x) top and bottom, leaving 3^x = 3, so => x=1
3^x (6^x-3^x)/(6^x-3^x)=3
3^x=3
X=1; as simple as this
Х=1
(18^x - 9^x) / (6^x - 3^x) = 3
-------------------------------------------------------------------------------------------------------
9^x(2^x - 1) / 3^x(2^x-1)) factor out 9^x on top and 3^x on bot
9^x / 3^x cancel out (2^x-1)/(2^x-1)) = 1
(9/3)^x property: a^x/b^x -> (a/b)^x
3^x = 3 9/3 = 3
x = 1 property: a^b = a -> a=1
done in 1 minute with no music
I'm sorry but there is NO WAY that this is a math Olympiad question !!!
I solved it using basic algebra rules in about 23 seconds... CLICKBAIT NONSENSE>>>!
Math Olympiad exam is conducted for every grade of students. So, this is actually a math olympiad problem. This channel is dedicated to math olympiads for grade 10 or lower. On my second channel math booster, i cover math olympiad problems for grade 12 students.
Х = 1