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

The answer to log_{5}(y)=4-4log_{y}(5) is y=25

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

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

y = 25

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{5} (y) = u

u = 4 - \frac{4}{u}

Solve

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

u = 2

Substitute back

u = lo g_{5} (y),

solve for

y

Solve

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

y = 25

Verify Solutions:

y = 25

True

The solution is

y = 25

lo g_{10} (x + 4) + lo g_{10} (x) = 9

4 ln (2 x + 9) + 5 = 29

lo g_{x} (9 x - 20) = 2

x, ln (x^{2}) = 4

ln (4 x - 1) - 3 ln (9) = 2 ln (3)

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