What is the answer to (ye^y-9y)/(e^y)=0 ?

The answer to (ye^y-9y)/(e^y)=0 is y=0,y=2ln(3)

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(ye^y-9y)/(e^y)=0

\frac{y e ^{y} - 9 y}{e ^{y}} = 0

y = 0, y = 2 ln (3)

Solution steps

\frac{y e ^{y} - 9 y}{e ^{y}} = 0

Apply exponent rules

(y e^{y} - 9 y) e^{- y} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y e^{y} - 9 y = 0 or e^{- y} = 0

Solve

y e^{y} - 9 y = 0 : y = 0, y = 2 ln (3)

Solve

e^{- y} = 0 :

No Solution for

y \in R

Verify Solutions:

y = 0

True

, y = 2 ln (3)

True

The solutions are

y = 0, y = 2 ln (3)

3 2^{x} = \frac{1}{4}

(\frac{1}{2})^{x} = x

4^{x - 1} = 16

2^{2 x} + 2^{x + 1} = 80

8^{y} = 32

What is the answer to (ye^y-9y)/(e^y)=0 ?
The answer to (ye^y-9y)/(e^y)=0 is y=0,y=2ln(3)