What is the answer to y^{log_{10}(y)}=100y ?

The answer to y^{log_{10}(y)}=100y is y=100,y= 1/10

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y^{log_{10}(y)}=100y

y^{l o g_{10} (y)} = 100 y

y = 100, y = \frac{1}{10}

Decimal Notation

y = 100, y = 0.1

Solution steps

y^{l o g_{10} (y)} = 100 y

Apply log rules

lo g_{10} (y) lo g_{10} (y) = lo g_{10} (y) + 2

Rewrite the equation with

lo g_{10} (y) = u

uu = u + 2

Solve

uu = u + 2 : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = lo g_{10} (y),

solve for

y

Solve

lo g_{10} (y) = 2 : y = 100

Solve

lo g_{10} (y) = - 1 : y = \frac{1}{10}

y = 100, y = \frac{1}{10}

Verify Solutions:

y = 100

True

, y = \frac{1}{10}

True

The solutions are

y = 100, y = \frac{1}{10}

0.84 = lo g_{10} (x)

lo g_{x} (81) = 3

ln (x^{3}) = 18

lo g_{10} (x^{2} - 3 x) = 1

lo g_{10} (5 x + 150) = 3

What is the answer to y^{log_{10}(y)}=100y ?
The answer to y^{log_{10}(y)}=100y is y=100,y= 1/10
Solve for y: y^{log_{10}(y)}=100y
The solution is y=100,y= 1/10