What is the answer to log_{2}(y)-8*log_{y}(2)=2 ?

The answer to log_{2}(y)-8*log_{y}(2)=2 is y=16,y= 1/4

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log_{2}(y)-8*log_{y}(2)=2

lo g_{2} (y) - 8 \cdot lo g_{y} (2) = 2

y = 16, y = \frac{1}{4}

Decimal Notation

y = 16, y = 0.25

Solution steps

lo g_{2} (y) - 8 lo g_{y} (2) = 2

Apply log rules

lo g_{2} (y) - \frac{8}{lo g _{2} ( y )} = 2

Rewrite the equation with

lo g_{2} (y) = u

u - \frac{8}{u} = 2

Solve

u - \frac{8}{u} = 2 : u = 4, u = - 2

u = 4, u = - 2

Substitute back

u = lo g_{2} (y),

solve for

y

Solve

lo g_{2} (y) = 4 : y = 16

Solve

lo g_{2} (y) = - 2 : y = \frac{1}{4}

y = 16, y = \frac{1}{4}

Verify Solutions:

y = 16

True

, y = \frac{1}{4}

True

The solutions are

y = 16, y = \frac{1}{4}

lo g_{10} (x - 2) + lo g_{10} (x - 3) = lo g_{10} (2)

lo g_{2} (x + 5) - lo g_{2} (x - 1) = 2

b, lo g_{3} (\frac{a}{b}) = lo g_{27} (a) + 1

lo g_{9} (x - 5) + lo g_{9} (x + 3) = 1

lo g_{a} (x) = \frac{1}{b \cdot lo g _{a} ( c )}

What is the answer to log_{2}(y)-8*log_{y}(2)=2 ?
The answer to log_{2}(y)-8*log_{y}(2)=2 is y=16,y= 1/4
Solve for y: log_{2}(y)-8*log_{y}(2)=2
The solution is y=16,y= 1/4