What is the answer to 2^{x+1}+2^{3x}=5*2^{x+4} ?

The answer to 2^{x+1}+2^{3x}=5*2^{x+4} is x=(ln(78))/(2ln(2))

Solve for x: 2^{x+1}+2^{3x}=5*2^{x+4}

The solution is x=(ln(78))/(2ln(2))

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2^{x + 1} + 2^{3 x} = 5 \cdot 2^{x + 4}

x = \frac{ln ( 78 )}{2 ln ( 2 )}

Decimal Notation

x = 3.14270 \dots

Solution steps

2^{x + 1} + 2^{3 x} = 5 \cdot 2^{x + 4}

Apply exponent rules

2^{x} \cdot 2^{1} + (2^{x})^{3} = 5 \cdot 2^{x} \cdot 2^{4}

Rewrite the equation with

2^{x} = u

u \cdot 2^{1} + (u)^{3} = 5 u \cdot 2^{4}

Solve

u \cdot 2^{1} + u^{3} = 5 u \cdot 2^{4} : u = 0, u = - 78, u = 78

u = 0, u = - 78, u = 78

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 0 :

No Solution for

x \in R

Solve

2^{x} = - 78 :

No Solution for

x \in R

Solve

2^{x} = 78 : x = \frac{ln ( 78 )}{2 ln ( 2 )}

x = \frac{ln ( 78 )}{2 ln ( 2 )}

2^{x + 1} = 8^{x}

x, 2^{2 x} - 2^{x + 1} = 0

x, t (x) = e^{x}

2 5^{x} - 3 \cdot 5^{x} = 0

3^{2 x - 7} = 81

What is the answer to 2^{x+1}+2^{3x}=5*2^{x+4} ?
The answer to 2^{x+1}+2^{3x}=5*2^{x+4} is x=(ln(78))/(2ln(2))
Solve for x: 2^{x+1}+2^{3x}=5*2^{x+4}
The solution is x=(ln(78))/(2ln(2))