What is the answer to (e^y-1)/(2-3e^y)= 2/7 ?

The answer to (e^y-1)/(2-3e^y)= 2/7 is y=ln(11/13)

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(e^y-1)/(2-3e^y)= 2/7

\frac{e ^{y} - 1}{2 - 3 e ^{y}} = \frac{2}{7}

y = ln (\frac{11}{13})

Decimal Notation

y = - 0.16705 \dots

Solution steps

\frac{e ^{y} - 1}{2 - 3 e ^{y}} = \frac{2}{7}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(e^{y} - 1) \cdot 7 = (2 - 3 e^{y}) \cdot 2

Expand

(e^{y} - 1) \cdot 7 : 7 e^{y} - 7

Expand

(2 - 3 e^{y}) \cdot 2 : 4 - 6 e^{y}

7 e^{y} - 7 = 4 - 6 e^{y}

Move

7

to the right side

7 e^{y} = - 6 e^{y} + 11

Move

6 e^{y}

to the left side

13 e^{y} = 11

Divide both sides by

13

e^{y} = \frac{11}{13}

Apply exponent rules

y = ln (\frac{11}{13})

Verify Solutions:

y = ln (\frac{11}{13})

True

The solution is

y = ln (\frac{11}{13})

4^{x + 1} = 25 6^{1}

a^{2 x}

4^{x} = 8^{5 - x}

3 2^{x - 3} = 1 6^{x - 5}

3 \cdot 3^{x} - 2 \cdot 3^{- x} = 1

What is the answer to (e^y-1)/(2-3e^y)= 2/7 ?
The answer to (e^y-1)/(2-3e^y)= 2/7 is y=ln(11/13)