What is the answer to 2log_{4}(x)+2log_{x}(4)=5 ?

The answer to 2log_{4}(x)+2log_{x}(4)=5 is x=16,x=2

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2log_{4}(x)+2log_{x}(4)=5

2 lo g_{4} (x) + 2 lo g_{x} (4) = 5

x = 16, x = 2

Solution steps

2 lo g_{4} (x) + 2 lo g_{x} (4) = 5

Apply log rules

2 lo g_{4} (x) + \frac{2}{lo g _{4} ( x )} = 5

Rewrite the equation with

lo g_{4} (x) = u

2 u + \frac{2}{u} = 5

Solve

2 u + \frac{2}{u} = 5 : u = 2, u = \frac{1}{2}

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

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 2 : x = 16

Solve

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

x = 16, x = 2

Verify Solutions:

x = 16

True

, x = 2

True

The solutions are

x = 16, x = 2

lo g_{2} (x + 3) + lo g_{2} (x + 5) = 3

lo g_{e} (x + 2) - lo g_{e} (3 x) = 0

lo g_{10} (9 x) + lo g_{10} (3 x) = 3

lo g_{2 x} (81) = \frac{4}{3}

lo g_{10} (x) = - 4.67

What is the answer to 2log_{4}(x)+2log_{x}(4)=5 ?
The answer to 2log_{4}(x)+2log_{x}(4)=5 is x=16,x=2
Solve for x: 2log_{4}(x)+2log_{x}(4)=5
The solution is x=16,x=2