What is the answer to 2^{2x+3}=2^{x+1}+3 ?

The answer to 2^{2x+3}=2^{x+1}+3 is x=(ln(3/4))/(ln(2))

Solve for x: 2^{2x+3}=2^{x+1}+3

The solution is x=(ln(3/4))/(ln(2))

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2^{2 x + 3} = 2^{x + 1} + 3

x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

Decimal Notation

x = - 0.41503 \dots

Solution steps

2^{2 x + 3} = 2^{x + 1} + 3

Apply exponent rules

(2^{x})^{2} \cdot 2^{3} = 2^{x} \cdot 2^{1} + 3

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{3} = u \cdot 2^{1} + 3

Solve

u^{2} \cdot 2^{3} = u \cdot 2^{1} + 3 : u = \frac{3}{4}, u = - \frac{1}{2}

u = \frac{3}{4}, u = - \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = \frac{3}{4} : x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

Solve

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

No Solution for

x \in R

x = \frac{ln ( \frac{3}{4} )}{ln ( 2 )}

5^{x - 4} = 7^{5 x + 2}

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

7^{3 x - 17} = 4 9^{x}

(- 8)^{x} = - 125

1 2^{b} = 3

What is the answer to 2^{2x+3}=2^{x+1}+3 ?
The answer to 2^{2x+3}=2^{x+1}+3 is x=(ln(3/4))/(ln(2))
Solve for x: 2^{2x+3}=2^{x+1}+3
The solution is x=(ln(3/4))/(ln(2))