What is the answer to e^{x+1}+e^{x+2}= 1/pi ?

The answer to e^{x+1}+e^{x+2}= 1/pi is x=-ln(pi(1+e))-1

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e^{x+1}+e^{x+2}= 1/pi

e^{x + 1} + e^{x + 2} = \frac{1}{π}

x = - ln (π (1 + e)) - 1

Decimal Notation

x = - 3.45799 \dots

Solution steps

e^{x + 1} + e^{x + 2} = \frac{1}{π}

Factor

e^{x + 1} + e^{x + 2} : (1 + e) e^{1 + x}

(1 + e) e^{1 + x} = \frac{1}{π}

Divide both sides by

1 + e

e^{1 + x} = \frac{1}{π ( 1 + e )}

Apply exponent rules

1 + x = ln (\frac{1}{π ( 1 + e )})

Solve

1 + x = ln (\frac{1}{π ( 1 + e )}) : x = - ln (π (1 + e)) - 1

x = - ln (π (1 + e)) - 1

3^{2 x} - 4 (3^{x + 1}) + 27 = 0

\frac{( 1 + 0.18 ) ^{n} - 1}{0.18} = 10

2^{- x} = \frac{1}{64}

2^{x} + 2^{- x} = \frac{5}{2}

7^{8 x + 7} = 3

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