What is the answer to log_{2}(x)-log_{x}(4)=1 ?

The answer to log_{2}(x)-log_{x}(4)=1 is x=4,x= 1/2

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log_{2}(x)-log_{x}(4)=1

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

x = 4, x = \frac{1}{2}

Decimal Notation

x = 4, x = 0.5

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

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

Solve

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

u = 2, u = - 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

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

x = 4, x = \frac{1}{2}

Verify Solutions:

x = 4

True

, x = \frac{1}{2}

True

The solutions are

x = 4, x = \frac{1}{2}

lo g_{5} (x - 2) = lo g_{5} (3 x + 7)

lo g_{10} (x) + lo g_{10} (3) = 1

lo g_{x} (7 x - 10) = 2

2 lo g_{3} (x + 28) = 6

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

What is the answer to log_{2}(x)-log_{x}(4)=1 ?
The answer to log_{2}(x)-log_{x}(4)=1 is x=4,x= 1/2
Solve for x: log_{2}(x)-log_{x}(4)=1
The solution is x=4,x= 1/2