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Solve 5.4^x+1 - 16^x = 64

help me to find the value of x pls

5.4x + 1 - 16x = 64
or, 5.4x.4 - 42x = 64

Let 4x = a

or, 20a - a2 = 64
or, a2 - 20a + 64 = 0
or, a2 - (16 + 4)a + 64 = 0
or, a2 - 16a - 4a + 64 = 0
or, a(a - 16) -4(a - 16) = 0
or, (a - 16)(a - 4) = 0

Either, a = 16
so, 4x = 42
so, x = 2

OR, a = 4
so, 4x = 4
so, x = 1

Hence, x = 1, 2

dibas answered 2 years ago