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3 ^ (2x) - 2 ^ (x + 1) * 3 ^ x - 3 * 2 ^ (2x) = 0 .
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Sep 3, 2021
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3 ^ (2x) - 2 ^ (x + 1) * 3 ^ x - 3 * 2 ^ (2x) = 0 .
Mathematics
middle-school
Thousight
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Answer:
log₁.₅3 or 2.70951
Explanation:
3^(2x) - 2^(x + 1) * 3^x - 3*2^(2x) = 0
3^(2x)- 2*2^x*3^x + 2^(2x)- 4*2^(2x)=0
(3^x-2^x)^2 - (2*2^x)^2=0
(3^x-2^x+2*2^x)(3^x - 2^x - 2*2^x)=0
(3^x+2^x)(3^x- 3*2^x)=0
3^x+2^x>0 for any value of x
3^x- 3*2^x=0
3^x= 3*2^x
3^x/2^x=3
1.5^x=3
x= log₁.₅ 3 = 2.70951
Attila Fulop
answered
Sep 9, 2021
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Attila Fulop
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