What is the answer to 4log_{y}(2)+log_{2}(y)=4 ?

The answer to 4log_{y}(2)+log_{2}(y)=4 is y=4

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4log_{y}(2)+log_{2}(y)=4

4 lo g_{y} (2) + lo g_{2} (y) = 4

y = 4

Solution steps

4 lo g_{y} (2) + lo g_{2} (y) = 4

Apply log rules

\frac{4}{lo g _{2} ( y )} + lo g_{2} (y) = 4

Rewrite the equation with

lo g_{2} (y) = u

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

Solve

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

u = 2

Substitute back

u = lo g_{2} (y),

solve for

y

Solve

lo g_{2} (y) = 2 : y = 4

y = 4

Verify Solutions:

y = 4

True

The solution is

y = 4

10 lo g_{10} (x) = - 1

lo g_{4} (x + 3) + lo g_{4} (2 - x) = 1

ln (x) + ln (x - 2) = 3

x, ln (x + 1) = 2

4 ln (7 x + 3) + 12 = 40

What is the answer to 4log_{y}(2)+log_{2}(y)=4 ?
The answer to 4log_{y}(2)+log_{2}(y)=4 is y=4
Solve for y: 4log_{y}(2)+log_{2}(y)=4
The solution is y=4