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mawka75
@mawka75
August 2022
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[tex] 2*81^{x} - 3* 16^{x} = 36^{x} [/tex]
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kirichekov
Verified answer
2*81^x-3*16^x=36^x |: 36^x
2*(81^x:36^x)-3*(16^x:36^x)=36^x:36^x
2*(81/36)^x-3*(16/36)^x=1
2*(9/4)^x-3*(4/9)^x=1
замена переменных: (9/4)^x=t, t>0
2t-3/t=1 |*t
2t²-t-3=0. t₁=-1, -1<0 посторонний корень
t₂=3/2
обратная замена:
t=3/2. (9/4)^x=3/2. ((3/2)²)^x=(3/2)⁻¹. 2x=-1.
x=-0,5
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Verified answer
2*81^x-3*16^x=36^x |: 36^x2*(81^x:36^x)-3*(16^x:36^x)=36^x:36^x
2*(81/36)^x-3*(16/36)^x=1
2*(9/4)^x-3*(4/9)^x=1
замена переменных: (9/4)^x=t, t>0
2t-3/t=1 |*t
2t²-t-3=0. t₁=-1, -1<0 посторонний корень
t₂=3/2
обратная замена:
t=3/2. (9/4)^x=3/2. ((3/2)²)^x=(3/2)⁻¹. 2x=-1. x=-0,5