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

help me to find the value of x pls

Go to main content# Solve 5.4^x+1 - 16^x = 64

help me to find the value of x pls

5.4^{x + 1} - 16^{x} = 64

or, 5.4^{x}.4 - 4^{2x} = 64

Let 4^{x} = a

or, 20a - a^{2} = 64

or, a^{2} - 20a + 64 = 0

or, a^{2} - (16 + 4)a + 64 = 0

or, a^{2} - 16a - 4a + 64 = 0

or, a(a - 16) -4(a - 16) = 0

or, (a - 16)(a - 4) = 0

Either, a = 16

so, 4^{x} = 4^{2}

so, x = 2

OR, a = 4

so, 4^{x} = 4

so, x = 1

Hence, x = 1, 2