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Popular >

e^x+12e^{-x}=7

Solution

e^{x} + 12 e^{- x} = 7

Solution

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

+1

Decimal Notation

x = 1.38629 \dots, x = 1.09861 \dots

Solution steps

e^{x} + 12 e^{- x} = 7

Apply exponent rules

e^{x} + 12 (e^{x})^{- 1} = 7

Rewrite the equation with

e^{x} = u

u + 12 (u)^{- 1} = 7

Solve

u + 12 u^{- 1} = 7 : u = 4, u = 3

u = 4, u = 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 4 : x = 2 ln (2)

Solve

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

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

Popular Examples

10^{2x^2-10x+1}=e

1 0^{2 x^{2} - 10 x + 1} = e

2^{5^{x-3}}=2^{25^x}

2^{5^{x - 3}} = 2^{2 5^{x}}

e^{2x}-4*e^x+4=0

e^{2 x} - 4 \cdot e^{x} + 4 = 0

4^{x^2}-2^{x^2}=240

4^{x^{2}} - 2^{x^{2}} = 240

solvefor x,xy=e^{x+y}solve for

x, x y = e^{x + y}

Frequently Asked Questions (FAQ)

What is the answer to e^x+12e^{-x}=7 ?
The answer to e^x+12e^{-x}=7 is x=2ln(2),x=ln(3)