What is the answer to log_{y}(y-2)+log_{y}(y+5)=2 ?

The answer to log_{y}(y-2)+log_{y}(y+5)=2 is y= 10/3

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log_{y}(y-2)+log_{y}(y+5)=2

lo g_{y} (y - 2) + lo g_{y} (y + 5) = 2

y = \frac{10}{3}

Decimal Notation

y = 3.33333 \dots

Solution steps

lo g_{y} (y - 2) + lo g_{y} (y + 5) = 2

Apply log rules

\frac{ln ( ( y - 2 ) ( y + 5 ) )}{ln ( y )} = 2

Multiply both sides by

ln (y)

\frac{ln ( ( y - 2 ) ( y + 5 ) )}{ln ( y )} ln (y) = 2 ln (y)

Simplify

ln ((y - 2) (y + 5)) = 2 ln (y)

Apply log rules

(y - 2) (y + 5) = y^{2}

Solve

(y - 2) (y + 5) = y^{2} : y = \frac{10}{3}

y = \frac{10}{3}

Verify Solutions:

y = \frac{10}{3}

True

The solution is

y = \frac{10}{3}

lo g_{x} (\frac{1}{16}) = - 4

30 = 10 lo g_{10} (x)

2 lo g_{3} (n) + 3 lo g_{27} (n) = 15

lo g_{3} (y) = 5

- 3 = 20 lo g_{10} (\frac{x}{1})

What is the answer to log_{y}(y-2)+log_{y}(y+5)=2 ?
The answer to log_{y}(y-2)+log_{y}(y+5)=2 is y= 10/3
Solve for y: log_{y}(y-2)+log_{y}(y+5)=2
The solution is y= 10/3