if 4^x-4^(x-1)=24 ,then find the value of (2x)^x .
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Heya
4^x-4^(x-1) = 24
4^x - (4^x/4¹) = 24
(4×4^x - 4^x)/4 = 24
3×4^x/4 = 24
4^x = 24×4/3
4^x = 32
2^2x = 2^5
Equating the powers,
2x = 5
x = 5/2
(2x)^x = (2×5/2)^5/2
= 5^(5/2)
= 5^5/5²
= 5³ = 125.
Hope it helps! ^_^
4^x-4^(x-1) = 24
4^x - (4^x/4¹) = 24
(4×4^x - 4^x)/4 = 24
3×4^x/4 = 24
4^x = 24×4/3
4^x = 32
2^2x = 2^5
Equating the powers,
2x = 5
x = 5/2
(2x)^x = (2×5/2)^5/2
= 5^(5/2)
= 5^5/5²
= 5³ = 125.
Hope it helps! ^_^
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