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Popular >

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

Solution

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

Solution

x = ln (1.21341 \dots)

+1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

u^{2} + 1 = 3 u^{- 1} : u \approx 1.21341 \dots

u \approx 1.21341 \dots

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 1.21341 \dots : x = ln (1.21341 \dots)

x = ln (1.21341 \dots)

Popular Examples

5^{5 x - 2} = 45

5^x=\sqrt[3]{25}

6^{x} = 3^{x + 2}

1 0^{a} = 33

(5^9)/(5^3)=5^a

\frac{5 ^{9}}{5 ^{3}} = 5^{a}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}+1=3e^{-x} ?
The answer to e^{2x}+1=3e^{-x} is x=ln(1.21341…)