What is the answer to log_{5}(y)=4log_{y}(5) ?

The answer to log_{5}(y)=4log_{y}(5) is y=25,y= 1/25

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log_{5}(y)=4log_{y}(5)

lo g_{5} (y) = 4 lo g_{y} (5)

y = 25, y = \frac{1}{25}

Decimal Notation

y = 25, y = 0.04

Solution steps

lo g_{5} (y) = 4 lo g_{y} (5)

Apply log rules

lo g_{5} (y) = \frac{4}{lo g _{5} ( y )}

Rewrite the equation with

lo g_{5} (y) = u

u = \frac{4}{u}

Solve

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

u = 2, u = - 2

Substitute back

u = lo g_{5} (y),

solve for

y

Solve

lo g_{5} (y) = 2 : y = 25

Solve

lo g_{5} (y) = - 2 : y = \frac{1}{25}

y = 25, y = \frac{1}{25}

Verify Solutions:

y = 25

True

, y = \frac{1}{25}

True

The solutions are

y = 25, y = \frac{1}{25}

10 lo g_{10} (x) = 40

lo g_{x} (9) = \frac{1}{2}

20 lo g_{10} (g) = 12

ln (4 x + 3) = 5

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

What is the answer to log_{5}(y)=4log_{y}(5) ?
The answer to log_{5}(y)=4log_{y}(5) is y=25,y= 1/25
Solve for y: log_{5}(y)=4log_{y}(5)
The solution is y=25,y= 1/25