What is the answer to 4^x+64=16*2^x ?

The answer to 4^x+64=16*2^x is x=3

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4^x+64=16*2^x

4^{x} + 64 = 16 \cdot 2^{x}

x = 3

Solution steps

4^{x} + 64 = 16 \cdot 2^{x}

Apply exponent rules

(2^{x})^{2} + 64 = 16 \cdot 2^{x}

Rewrite the equation with

2^{x} = u

(u)^{2} + 64 = 16 u

Solve

u^{2} + 64 = 16 u : u = 8

u = 8

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

x = 3

b, e^{a x} - e^{b - a x} = c

t = 20 + 70 e^{- t}

x, z = y^{3} e^{x^{2}}

5^{5 x - 2} = 40

10 e^{- 0.03 x} = 4