What is the answer to 2log_{4}(x)+log_{x}(4)=3 ?

The answer to 2log_{4}(x)+log_{x}(4)=3 is x=4,x=2

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2log_{4}(x)+log_{x}(4)=3

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

x = 4, x = 2

Solution steps

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

Apply log rules

2 lo g_{4} (x) + \frac{1}{lo g _{4} ( x )} = 3

Rewrite the equation with

lo g_{4} (x) = u

2 u + \frac{1}{u} = 3

Solve

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

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

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 1 : x = 4

Solve

lo g_{4} (x) = \frac{1}{2} : x = 2

x = 4, x = 2

Verify Solutions:

x = 4

True

, x = 2

True

The solutions are

x = 4, x = 2

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

lo g_{6} (2 x) - lo g_{6} (x + 1) = 0

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

ln (x) = ln (x)

y, ln (y) = ln (x) + c

What is the answer to 2log_{4}(x)+log_{x}(4)=3 ?
The answer to 2log_{4}(x)+log_{x}(4)=3 is x=4,x=2
Solve for x: 2log_{4}(x)+log_{x}(4)=3
The solution is x=4,x=2