Log2²x + 3log2 x - 4 = 0

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To solve the equation Log2²x + 3log2 x - 4 = 0, we can use the properties of logarithms to rewrite it in a simpler form.

Let's start by using the property that states loga (mn) = loga m + loga n.

So, we rewrite the equation as:

2log2 x + log2 x - 4 = 0

Now, we can combine like terms:

3log2 x - 4 = 0

Next, we can use the property that states loga (a) = 1

So, we can rewrite the equation as:

3log2 x - log2 16 = 0

Now, we simplify further:

log2 x^3 - log2 16 = 0

Using the property that states loga m - loga n = loga (m/n), we simplify to:

log2 (x^3/16) = 0

Now, we can rewrite the equation in exponential form:

2^0 = x^3/16

1 = x^3/16

16 = x^3

Taking the cubic root of both sides, we get:

x = 2

So, the solution to the equation Log2²x + 3log2 x - 4 = 0 is x = 2.