What is the answer to 3log_{5}(y)-log_{y}(5)=2 ?

The answer to 3log_{5}(y)-log_{y}(5)=2 is y=5,y= 1/(\sqrt[3]{5)}

Solve for y: 3log_{5}(y)-log_{y}(5)=2

The solution is y=5,y= 1/(\sqrt[3]{5)}

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

Decimal Notation

y = 5, y = 0.58480 \dots

Solution steps

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

Apply log rules

3 lo g_{5} (y) - \frac{1}{lo g _{5} ( y )} = 2

Rewrite the equation with

lo g_{5} (y) = u

3 u - \frac{1}{u} = 2

Solve

3 u - \frac{1}{u} = 2 : u = 1, u = - \frac{1}{3}

u = 1, u = - \frac{1}{3}

Substitute back

u = lo g_{5} (y),

solve for

y

Solve

lo g_{5} (y) = 1 : y = 5

Solve

Verify Solutions:

y = 5

True

The solutions are

lo g_{4} (x + 3) = lo g_{4} (3 x - 7)

1 0^{7 l o g_{10} (x)} = 7 x

35000 = 95858 ln (x) - 991636

lo g_{4} (2 - x) = lo g_{16} (25)

- 6 + lo g_{10} (x - 1) = lo g_{10} (5)

What is the answer to 3log_{5}(y)-log_{y}(5)=2 ?
The answer to 3log_{5}(y)-log_{y}(5)=2 is y=5,y= 1/(\sqrt[3]{5)}
Solve for y: 3log_{5}(y)-log_{y}(5)=2
The solution is y=5,y= 1/(\sqrt[3]{5)}