What is the answer to (e^x+9)/(e^{-x)+5}=2 ?

The answer to (e^x+9)/(e^{-x)+5}=2 is x=ln(2)

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(e^x+9)/(e^{-x)+5}=2

\frac{e ^{x} + 9}{e ^{- x} + 5} = 2

x = ln (2)

Decimal Notation

x = 0.69314 \dots

Solution steps

\frac{e ^{x} + 9}{e ^{- x} + 5} = 2

Multiply both sides by

e^{- x} + 5

\frac{e ^{x} + 9}{e ^{- x} + 5} (e^{- x} + 5) = 2 (e^{- x} + 5)

Simplify

e^{x} + 9 = 2 (e^{- x} + 5)

Apply exponent rules

e^{x} + 9 = 2 ((e^{x})^{- 1} + 5)

Rewrite the equation with

e^{x} = u

u + 9 = 2 ((u)^{- 1} + 5)

Solve

u + 9 = 2 (u^{- 1} + 5) : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = - 1 :

No Solution for

x \in R

x = ln (2)

Verify Solutions:

x = ln (2)

True

The solution is

x = ln (2)

4 \cdot 2^{x} = 5

\frac{3 ^{x} + 3 ^{- x}}{3 ^{x} - 3 ^{- x}} = 20

4 \times e^{2.7 x} = 33

4^{x + 2} = 8

e^{2 x} - 8 e^{x} = 20

What is the answer to (e^x+9)/(e^{-x)+5}=2 ?
The answer to (e^x+9)/(e^{-x)+5}=2 is x=ln(2)