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Popular >

2e^x+3e^{-x}=7

Solution

2 e^{x} + 3 e^{- x} = 7

Solution

x = ln (3), x = - ln (2)

+1

Decimal Notation

x = 1.09861 \dots, x = - 0.69314 \dots

Solution steps

2 e^{x} + 3 e^{- x} = 7

Apply exponent rules

2 e^{x} + 3 (e^{x})^{- 1} = 7

Rewrite the equation with

e^{x} = u

2 u + 3 (u)^{- 1} = 7

Solve

2 u + 3 u^{- 1} = 7 : u = 3, u = \frac{1}{2}

u = 3, u = \frac{1}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = ln (3)

Solve

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

x = ln (3), x = - ln (2)

Popular Examples

8^{x} = \frac{1}{2}

8 1^{x} = 243

3^{x + 1} = 4

3^x*2^{2x-3}=18

3^{x} \cdot 2^{2 x - 3} = 18

4^{x + 1} = \frac{1}{64}

Frequently Asked Questions (FAQ)

What is the answer to 2e^x+3e^{-x}=7 ?
The answer to 2e^x+3e^{-x}=7 is x=ln(3),x=-ln(2)