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Popular >

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

Solution

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

Solution

x = ln (0.68232 \dots)

+1

Decimal Notation

x = - 0.38224 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

u + (u)^{3} = 1

Solve

u + u^{3} = 1 : u \approx 0.68232 \dots

u \approx 0.68232 \dots

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 0.68232 \dots : x = ln (0.68232 \dots)

x = ln (0.68232 \dots)

Popular Examples

4^{- x + 3} = 8

8^{x} + \frac{1}{8 ^{x}} = 9

7^{2 + x} = 98

2^{x^{3}} = 12 8^{x}

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

Frequently Asked Questions (FAQ)

What is the answer to e^x+e^{3x}=1 ?
The answer to e^x+e^{3x}=1 is x=ln(0.68232…)