What is the answer to log_{4}(x)+log_{x}(4)=2.5 ?

The answer to log_{4}(x)+log_{x}(4)=2.5 is x=16,x=2

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log_{4}(x)+log_{x}(4)=2.5

lo g_{4} (x) + lo g_{x} (4) = 2.5

x = 16, x = 2

Solution steps

lo g_{4} (x) + lo g_{x} (4) = 2.5

Apply log rules

lo g_{4} (x) + \frac{1}{lo g _{4} ( x )} = 2.5

Rewrite the equation with

lo g_{4} (x) = u

u + \frac{1}{u} = 2.5

Solve

u + \frac{1}{u} = 2.5 : 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_{10} (x) + lo g_{10} (8) = 2

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

lo g_{a} (8) = 3

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

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

What is the answer to log_{4}(x)+log_{x}(4)=2.5 ?
The answer to log_{4}(x)+log_{x}(4)=2.5 is x=16,x=2
Solve for x: log_{4}(x)+log_{x}(4)=2.5
The solution is x=16,x=2