What is the answer to log_{3}(y)+4log_{y}(3)=4 ?

The answer to log_{3}(y)+4log_{y}(3)=4 is y=9

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log_{3}(y)+4log_{y}(3)=4

lo g_{3} (y) + 4 lo g_{y} (3) = 4

y = 9

Solution steps

lo g_{3} (y) + 4 lo g_{y} (3) = 4

Apply log rules

lo g_{3} (y) + \frac{4}{lo g _{3} ( y )} = 4

Rewrite the equation with

lo g_{3} (y) = u

u + \frac{4}{u} = 4

Solve

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

u = 2

Substitute back

u = lo g_{3} (y),

solve for

y

Solve

lo g_{3} (y) = 2 : y = 9

y = 9

Verify Solutions:

y = 9

True

The solution is

y = 9

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

lo g_{10} (4 x) + lo g_{10} (8 x) = 1

lo g_{2} (n) = 3.6 \cdot 1 0^{13}

ln (x - 1) + ln (x + 1) = ln (3)

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

What is the answer to log_{3}(y)+4log_{y}(3)=4 ?
The answer to log_{3}(y)+4log_{y}(3)=4 is y=9
Solve for y: log_{3}(y)+4log_{y}(3)=4
The solution is y=9