What is the answer to y^{3log_{10}(y)}=100y ?

The answer to y^{3log_{10}(y)}=100y is y=10,y= 1/(10^{2/3)}

Solve for y: y^{3log_{10}(y)}=100y

The solution is y=10,y= 1/(10^{2/3)}

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y^{3 l o g_{10} (y)} = 100 y

y = 10, y = \frac{1}{1 0 ^{\frac{2}{3}}}

Decimal Notation

y = 10, y = 0.21544 \dots

Solution steps

y^{3 l o g_{10} (y)} = 100 y

Apply log rules

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

Rewrite the equation with

lo g_{10} (y) = u

3 uu = u + 2

Solve

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

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

Substitute back

u = lo g_{10} (y),

solve for

y

Solve

lo g_{10} (y) = 1 : y = 10

Solve

lo g_{10} (y) = - \frac{2}{3} : y = \frac{1}{1 0 ^{\frac{2}{3}}}

y = 10, y = \frac{1}{1 0 ^{\frac{2}{3}}}

Verify Solutions:

y = 10

True

, y = \frac{1}{1 0 ^{\frac{2}{3}}}

True

The solutions are

y = 10, y = \frac{1}{1 0 ^{\frac{2}{3}}}

lo g_{x} (27) = \frac{3}{4}

lo g_{3} (2 x - 6) = 2

lo g_{10} (- x - 4) + lo g_{10} (3) = 1

lo g_{2} (x + 7) + lo g_{2} (x + 5) = 3

ln (x) + ln (x + 2) = ln (8)

What is the answer to y^{3log_{10}(y)}=100y ?
The answer to y^{3log_{10}(y)}=100y is y=10,y= 1/(10^{2/3)}
Solve for y: y^{3log_{10}(y)}=100y
The solution is y=10,y= 1/(10^{2/3)}