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Popular >

3e^x=1-2e^{0.5x}

Solution

3 e^{x} = 1 - 2 e^{0.5 x}

Solution

x = - 2 ln (3)

+1

Decimal Notation

x = - 2.19722 \dots

Solution steps

3 e^{x} = 1 - 2 e^{0.5 x}

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

3 u = 1 - 2 u

Solve

3 u = 1 - 2 u : u = \frac{1}{9}

u = \frac{1}{9}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{1}{9} : x = - 2 ln (3)

x = - 2 ln (3)

Popular Examples

sqrt(5)=5^{x+4}

5 = 5^{x + 4}

e^{x + 1} = 0

6^x+4(6^{-x})=5

6^{x} + 4 (6^{- x}) = 5

(\frac{2}{3})^{x} = 1

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

Frequently Asked Questions (FAQ)

What is the answer to 3e^x=1-2e^{0.5x} ?
The answer to 3e^x=1-2e^{0.5x} is x=-2ln(3)