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

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

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

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

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

Decimal Notation

y = - 0.09963 \dots

Solution steps

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

Add

11 e^{5 - 10 y}

to both sides

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

Simplify

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

Apply exponent rules

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

Solve

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

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

2^{4 x - 2} = 3

4^{x} = 6^{x + 2}

3 6^{x} = 6

2^{x - 1} + 2^{x} = 48

(7)^{6 x} = 4 9^{x - 6}

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