What is the answer to log_{2}(x)-8log_{x^2}(2)=3 ?

The answer to log_{2}(x)-8log_{x^2}(2)=3 is x=16,x= 1/2

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log_{2}(x)-8log_{x^2}(2)=3

lo g_{2} (x) - 8 lo g_{x^{2}} (2) = 3

x = 16, x = \frac{1}{2}

Decimal Notation

x = 16, x = 0.5

Solution steps

lo g_{2} (x) - 8 lo g_{x^{2}} (2) = 3

Apply log rules

lo g_{2} (x) - \frac{8}{2 lo g _{2} ( x )} = 3

Rewrite the equation with

lo g_{2} (x) = u

u - \frac{8}{2 u} = 3

Solve

u - \frac{8}{2 u} = 3 : u = 4, u = - 1

u = 4, u = - 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

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

Solve

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

x = 16, x = \frac{1}{2}

Verify Solutions:

x = 16

True

, x = \frac{1}{2}

True

The solutions are

x = 16, x = \frac{1}{2}

lo g_{2} (x + 6) = 5

lo g_{9} (x - 2) = 2

lo g_{a} (\frac{16}{81}) = - 4

ln (x + 5) + ln (x - 3) = 2 ln (x)

lo g_{2} (2 X) = 5

What is the answer to log_{2}(x)-8log_{x^2}(2)=3 ?
The answer to log_{2}(x)-8log_{x^2}(2)=3 is x=16,x= 1/2
Solve for x: log_{2}(x)-8log_{x^2}(2)=3
The solution is x=16,x= 1/2