What is the answer to 2^{2x+2}+3=2^{x+3} ?

The answer to 2^{2x+2}+3=2^{x+3} is x=(ln(3/2))/(ln(2)),x=-1

Solve for x: 2^{2x+2}+3=2^{x+3}

The solution is x=(ln(3/2))/(ln(2)),x=-1

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

x = \frac{ln ( \frac{3}{2} )}{ln ( 2 )}, x = - 1

Decimal Notation

x = 0.58496 \dots, x = - 1

Solution steps

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

Apply exponent rules

(2^{x})^{2} \cdot 2^{2} + 3 = 2^{x} \cdot 2^{3}

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{2} + 3 = u \cdot 2^{3}

Solve

u^{2} \cdot 2^{2} + 3 = u \cdot 2^{3} : u = \frac{3}{2}, u = \frac{1}{2}

u = \frac{3}{2}, u = \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{3}{2} : x = \frac{ln ( \frac{3}{2} )}{ln ( 2 )}

Solve

2^{x} = \frac{1}{2} : x = - 1

x = \frac{ln ( \frac{3}{2} )}{ln ( 2 )}, x = - 1

2 = e^{c}

4^{x} - 5 \cdot 2^{x} + 6 = 0

g (e^{n} - 1) = ln (e^{n} - 1 - 1)

2^{x} = e^{5}

5^{5 x + 1} = 12 5^{x}

What is the answer to 2^{2x+2}+3=2^{x+3} ?
The answer to 2^{2x+2}+3=2^{x+3} is x=(ln(3/2))/(ln(2)),x=-1
Solve for x: 2^{2x+2}+3=2^{x+3}
The solution is x=(ln(3/2))/(ln(2)),x=-1