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Popular >

0=2e^x-9e^{-3x}

Solution

0 = 2 e^{x} - 9 e^{- 3 x}

Solution

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

+1

Decimal Notation

x = 0.37601 \dots

Solution steps

0 = 2 e^{x} - 9 e^{- 3 x}

Add

9 e^{- 3 x}

to both sides

0 + 9 e^{- 3 x} = 2 e^{x} - 9 e^{- 3 x} + 9 e^{- 3 x}

Simplify

9 e^{- 3 x} = 2 e^{x}

Apply exponent rules

ln (9) - 3 x = ln (2) + x

Solve

ln (9) - 3 x = ln (2) + x : x = \frac{2 ln ( 3 ) - ln ( 2 )}{4}

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

Popular Examples

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

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

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

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

2 \cdot 3^{x} = 5

2 \cdot 1 0^{x} = 588

Frequently Asked Questions (FAQ)

What is the answer to 0=2e^x-9e^{-3x} ?
The answer to 0=2e^x-9e^{-3x} is x=(2ln(3)-ln(2))/4