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Popular >

e^x+45e^{-x}=14

Solution

e^{x} + 45 e^{- x} = 14

Solution

x = 2 ln (3), x = ln (5)

+1

Decimal Notation

x = 2.19722 \dots, x = 1.60943 \dots

Solution steps

e^{x} + 45 e^{- x} = 14

Apply exponent rules

e^{x} + 45 (e^{x})^{- 1} = 14

Rewrite the equation with

e^{x} = u

u + 45 (u)^{- 1} = 14

Solve

u + 45 u^{- 1} = 14 : u = 9, u = 5

u = 9, u = 5

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 9 : x = 2 ln (3)

Solve

e^{x} = 5 : x = ln (5)

x = 2 ln (3), x = ln (5)

Popular Examples

4 (\frac{1}{3})^{x} = 324

sqrt(9^{3x+1)}=3

9^{3 x + 1} = 3

1 6^{x - 5} = 128

3^{x+2}=9^{x-1}

3^{x + 2} = 9^{x - 1}

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

Frequently Asked Questions (FAQ)

What is the answer to e^x+45e^{-x}=14 ?
The answer to e^x+45e^{-x}=14 is x=2ln(3),x=ln(5)