What is the answer to solvefor x,ln(e^x-3)=2 ?

The answer to solvefor x,ln(e^x-3)=2 is x=ln(e^2+3)

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solvefor x,ln(e^x-3)=2

solve for

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

x = ln (e^{2} + 3)

Decimal Notation

x = 2.34075 \dots

Solution steps

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

Rewrite the equation with

e^{x} = u

ln (u - 3) = 2

Solve

ln (u - 3) = 2 : u = e^{2} + 3

u = e^{2} + 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = e^{2} + 3 : x = ln (e^{2} + 3)

x = ln (e^{2} + 3)

2^{x^{2} - 4 x - 12} = 8^{x + 2}

12 1^{2 x} = 1 1^{x + 3}

x, 3^{3 x - 2} = 9^{x}

a, 2^{a} = 3^{b}

5^{2 x} - 5^{x} - 6 = 0

What is the answer to solvefor x,ln(e^x-3)=2 ?
The answer to solvefor x,ln(e^x-3)=2 is x=ln(e^2+3)