Germany | Can you solve this ? | Math Olympiad X=?

[@에스피-z2g]

81×9^x-9^x=180 9^x=9/4 x=log9/log4 =log3/log2

[@markslowhand4214]

You can get the solution much faster by simply applying squareroot on both sides at 2:50. Then you are done by simply applying another log of base 3 on both sides.

[@gelbkehlchen]

Solution: 9^(x+1)-9^(x-1) = 20 |*9 ⟹ 81*9^x-9^x = 180 ⟹ 80*9^x = 180 |/80 ⟹ 9^x = 9/4 |ln() ⟹ x*ln(9) = ln(9/4) |/ln(9) ⟹ x = ln(9/4)/ln(9) ≈ 0.3691

[@ioannisimansola7115]

Too much fuss for something typical with logarithms

[@aines7958]

Parfait 👍👋🌹🇩🇿

[@rodicabrudea832]

I got 1 - log base 9 of 4

[@ТетянаВоронова-и8ц]

Цікаво

[@許金全-m6e]

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[@許金全-m6e]

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[@許金全-m6e]

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[@許金全-m6e]

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