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

The answer to log_{2}(x)=3log_{x}(2)+2 is x=8,x= 1/2

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

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

x = 8, x = \frac{1}{2}

Decimal Notation

x = 8, x = 0.5

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{2} (x) = u

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

Solve

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

u = 3, u = - 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 3 : x = 8

Solve

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

x = 8, x = \frac{1}{2}

Verify Solutions:

x = 8

True

, x = \frac{1}{2}

True

The solutions are

x = 8, x = \frac{1}{2}

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

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

lo g_{2} (x - 1) = 4 - lo g_{2} (3)

ln (5 - x) = ln (5) - ln (x)

a, lo g_{b} (a) = c

What is the answer to log_{2}(x)=3log_{x}(2)+2 ?
The answer to log_{2}(x)=3log_{x}(2)+2 is x=8,x= 1/2
Solve for x: log_{2}(x)=3log_{x}(2)+2
The solution is x=8,x= 1/2