What is the answer to 5e^x+48e^{-x}=46 ?

The answer to 5e^x+48e^{-x}=46 is x=3ln(2),x=ln(6/5)

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5e^x+48e^{-x}=46

5 e^{x} + 48 e^{- x} = 46

x = 3 ln (2), x = ln (\frac{6}{5})

Solution steps

5 e^{x} + 48 e^{- x} = 46

Apply exponent rules

5 e^{x} + 48 (e^{x})^{- 1} = 46

Rewrite the equation with

e^{x} = u

5 u + 48 (u)^{- 1} = 46

Solve

5 u + 48 u^{- 1} = 46 : u = 8, u = \frac{6}{5}

u = 8, u = \frac{6}{5}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 8 : x = 3 ln (2)

Solve

e^{x} = \frac{6}{5} : x = ln (\frac{6}{5})

x = 3 ln (2), x = ln (\frac{6}{5})

t, 45 x 1.07 1^{t} = 122

1 6^{x - 3} = 2^{x - 6}

n = 1. 2^{n}

2^{x} = 3.6 \cdot 1 0^{13}

9^{x - 2} = 240 + 9^{x}

What is the answer to 5e^x+48e^{-x}=46 ?
The answer to 5e^x+48e^{-x}=46 is x=3ln(2),x=ln(6/5)