What is the answer to (4^x+4)/5 =2^x ?

The answer to (4^x+4)/5 =2^x is x=2,x=0

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(4^x+4)/5 =2^x

\frac{4 ^{x} + 4}{5} = 2^{x}

x = 2, x = 0

Solution steps

\frac{4 ^{x} + 4}{5} = 2^{x}

Multiply both sides by

5

\frac{4 ^{x} + 4}{5} \cdot 5 = 2^{x} \cdot 5

Simplify

4^{x} + 4 = 2^{x} \cdot 5

Apply exponent rules

(2^{x})^{2} + 4 = 2^{x} \cdot 5

Rewrite the equation with

2^{x} = u

(u)^{2} + 4 = u \cdot 5

Solve

u^{2} + 4 = u \cdot 5 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = 1 : x = 0

x = 2, x = 0

(4) 5^{3 - x} - 7 = 2

4^{x} = 5^{2 x + 1}

x^{x^{3}} = 2^{2}

x, e^{x} + e^{- x} = 3

k, n = 2^{k}