What is the answer to sqrt(e^{2x)+9}-sqrt(e^{2x)-4}=1 ?

The answer to sqrt(e^{2x)+9}-sqrt(e^{2x)-4}=1 is x=(ln(40))/2

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sqrt(e^{2x)+9}-sqrt(e^{2x)-4}=1

e^{2 x} + 9 - e^{2 x} - 4 = 1

x = \frac{ln ( 40 )}{2}

Decimal Notation

x = 1.84443 \dots

Solution steps

e^{2 x} + 9 - e^{2 x} - 4 = 1

Rewrite the equation with

e^{2 x} = u

u + 9 - u - 4 = 1

Solve

u + 9 - u - 4 = 1 : u = 40

u = 40

Substitute back

u = e^{2 x},

solve for

x

Solve

e^{2 x} = 40 : x = \frac{ln ( 40 )}{2}

x = \frac{ln ( 40 )}{2}

\frac{e ^{4 x + 7}}{3} + 1 = 12

3 \cdot 9^{x} \cdot 2 7^{x} = 1

3^{3 x - 4} = 24 3^{x}

3^{2 x + 1} - 5 = 11

2 5^{x} = \frac{1}{5}

What is the answer to sqrt(e^{2x)+9}-sqrt(e^{2x)-4}=1 ?
The answer to sqrt(e^{2x)+9}-sqrt(e^{2x)-4}=1 is x=(ln(40))/2