log(2)X^2-log(2)x=log(4)4?

Question

solve for x if you wish

Answer 1

make it division
log(2) x^2/x=log(4)4
then simply...one of the x's counsel out
log(2) x=1 (anythin tht has da same base as the other number=1)
multiply both sides by 1/log (2)
cancelling it out so you get
x=1/log(2)

Answer 2

assuming you mean log(2) x is log (base 2) x

log(2)x² - log(2)x = log(4)4

Since log(a) (x^n) = n log (a) x
then log(2)x² = 2log(2)x

Also as log (a) a = 1 since (a) ^1 = a
then log(4)4 = 1

log(2)x² - log(2)x = log(4)4
→ 2log(2)x - log(2)x = 1

So log(2)x = 1

ie x = (2)^1 = 2

Answer 3

log(2)x^2 - log(2)x = log(4)4

Rule : logA - logB = log(A/B), if all to the same base.

Therefore, log(2)[x^2 / x] = log(4)4

or, log(2)x = log(4)4

But log(4)4 = 1.

So, log(2)x = 1

But 1 can be represented as log(2)2.

So, log(2)x = log(2)2

Take the antilog of both sides :

Thus, x = 2.

Answer 4

Let log(2) = c ( a constant)

With Substitution, we can rewrite the equation as:
c.x^2 - c.x = 2c.4
or x^2 - x - 8 = 0 ...(1)

This is a quardratic equation with solutions for
ax^2 + bx + c =0 as
[-b +/- sqrt(b^2 - 4.a.c) ]/2.a

Substituting in (1),
x = [1 +/- sqrt(1 + 4.8)] / 2
x = [1+/- sqrt(33)]/2