What is the answer to 5ln(7-e^{2x})=3 ?

The answer to 5ln(7-e^{2x})=3 is x=(ln(-e^{3/5}+7))/2

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5ln(7-e^{2x})=3

5 ln (7 - e^{2 x}) = 3

x = \frac{ln ( - e ^{\frac{3}{5}} + 7 )}{2}

Decimal Notation

x = 0.82219 \dots

Solution steps

5 ln (7 - e^{2 x}) = 3

Rewrite the equation with

e^{2 x} = u

5 ln (7 - u) = 3

Solve

5 ln (7 - u) = 3 : u = - e^{\frac{3}{5}} + 7

u = - e^{\frac{3}{5}} + 7

Substitute back

u = e^{2 x},

solve for

x

Solve

e^{2 x} = - e^{\frac{3}{5}} + 7 : x = \frac{ln ( - e ^{\frac{3}{5}} + 7 )}{2}

x = \frac{ln ( - e ^{\frac{3}{5}} + 7 )}{2}

2^{x + 2} = 32

e^{2 b} = 3 + b

2^{2 x} + 4^{x - 1} + 44 = 2^{2 x + 2}

7^{3 x - 2} = 11

4^{x} = 11

What is the answer to 5ln(7-e^{2x})=3 ?
The answer to 5ln(7-e^{2x})=3 is x=(ln(-e^{3/5}+7))/2