What is the answer to 3|2^x-1|=2^x ?

The answer to 3|2^x-1|=2^x is x=(ln(3/4))/(ln(2)),x=(ln(3/2))/(ln(2))

Solve for x: 3|2^x-1|=2^x

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

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3 ∣ 2^{x} - 1 ∣ = 2^{x}

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

Decimal Notation

x = - 0.41503 \dots, x = 0.58496 \dots

Solution steps

3 ∣ 2^{x} - 1 ∣ = 2^{x}

Rewrite the equation with

2^{x} = u

3 ∣ u - 1 ∣ = u

Solve

3 ∣ u - 1 ∣ = u : u = \frac{3}{4} or u = \frac{3}{2}

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

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

4^{x} + 4^{x + 1} = 20

3 x e^{x} + x^{2} e^{x} = 0

e^{4 x} = 2

2^{5 x + 3} = 3^{2 x + 1}

3^{x} 2^{3 x} = 4

What is the answer to 3|2^x-1|=2^x ?
The answer to 3|2^x-1|=2^x is x=(ln(3/4))/(ln(2)),x=(ln(3/2))/(ln(2))
Solve for x: 3|2^x-1|=2^x
The solution is x=(ln(3/4))/(ln(2)),x=(ln(3/2))/(ln(2))