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

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

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

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

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

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

\frac{4}{u} = u

Solve

\frac{4}{u} = u : u = 2, u = - 2

u = 2, u = - 2

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

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

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

Verify Solutions:

x = 4

True

, x = \frac{1}{4}

True

The solutions are

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

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

ln (4 - x) = 0

ln (x + 6) = - 1

lo g_{a} (n^{a}) = n

ln (x + 3) - ln (x) = ln (6)

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