What is the answer to 2e^{3x+8}-11e^{5-10x}=0 ?

The answer to 2e^{3x+8}-11e^{5-10x}=0 is x=(ln(11)-3-ln(2))/(13)

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2e^{3x+8}-11e^{5-10x}=0

2 e^{3 x + 8} - 11 e^{5 - 10 x} = 0

x = \frac{ln ( 11 ) - 3 - ln ( 2 )}{13}

Decimal Notation

x = - 0.09963 \dots

Solution steps

2 e^{3 x + 8} - 11 e^{5 - 10 x} = 0

Add

11 e^{5 - 10 x}

to both sides

2 e^{3 x + 8} - 11 e^{5 - 10 x} + 11 e^{5 - 10 x} = 0 + 11 e^{5 - 10 x}

Simplify

2 e^{3 x + 8} = 11 e^{5 - 10 x}

Apply exponent rules

ln (2) + 3 x + 8 = ln (11) + 5 - 10 x

Solve

ln (2) + 3 x + 8 = ln (11) + 5 - 10 x : x = \frac{ln ( 11 ) - 3 - ln ( 2 )}{13}

x = \frac{ln ( 11 ) - 3 - ln ( 2 )}{13}

15 = 10 (3^{(4 x - 10)}) - 25

t = 5 e^{2 t}

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

2^{n} = 1024

5^{4 x} = \frac{1}{5} 5

What is the answer to 2e^{3x+8}-11e^{5-10x}=0 ?
The answer to 2e^{3x+8}-11e^{5-10x}=0 is x=(ln(11)-3-ln(2))/(13)