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Popular >

ln(4e^{2x})=1

Solution

ln (4 e^{2 x}) = 1

Solution

x = \frac{1 - 2 ln ( 2 )}{2}

+1

Decimal Notation

x = - 0.19314 \dots

Solution steps

ln (4 e^{2 x}) = 1

Rewrite the equation with

e^{2 x} = u

ln (4 u) = 1

Solve

ln (4 u) = 1 : u = \frac{e}{4}

u = \frac{e}{4}

Substitute back

u = e^{2 x},

solve for

x

Solve

e^{2 x} = \frac{e}{4} : x = \frac{1 - 2 ln ( 2 )}{2}

x = \frac{1 - 2 ln ( 2 )}{2}

Popular Examples

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

5^{7x+4}=3^{x+2}

5^{7 x + 4} = 3^{x + 2}

e^{- 5 x} = 10

6 4^{x} - 8^{x} - 56 = 0

e^{x} + 4 e^{- x} = 5

Frequently Asked Questions (FAQ)

What is the answer to ln(4e^{2x})=1 ?
The answer to ln(4e^{2x})=1 is x=(1-2ln(2))/2