# Solve 4^x - 6.2^x+1 + 32 = 0

how to solve this

Go to main content# Solve 4^x - 6.2^x+1 + 32 = 0

how to solve this

You just need to separate the 2^x and substitute its value for some variable. And then substitute it back to the original value.

4^{x} - 6.2^{x + 1} + 32 = 0

or, 4^{x} - 6.2^{x}.2 + 32 = 0

or, 2^{2x} - 6.2^{x}.2 + 32 = 0

Let 2^{x} = a

or, a^{2} - 6.a.2 + 32 = 0

or, a^{2} - (8 + 4)a + 32 = 0

or, a^{2} - 8a - 4a + 32 = 0

or, a(a - 8) - 4(a - 8) = 0

or, (a - 8)(a - 4) = 0

Either a = 8

so, 2^{x} = 2^{3}

so, x = 3

OR, a = 4

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

∴ x = 2

Hence, x = 2, 3

Video explanation: