In this exercise we have to use the properties of the logarithm to write it in one way, like this:

From these recalling some properties of the logarithm, we find that:
- When the logarithm is equal to the base, the logarithm will always be equal to 1.
- Logarithm of any base, whose logarithm is equal to 1, will always have the result equal to 0.
- Two logarithms with the same base are equal when the logarithms are also equal.
given the equation as:

See more about logarithm at brainly.com/question/10486788
Hello oddworld7836!

Factor the expression into an equivalent form 12y² - 75.


By observing the expression, we can see that, 3 is the only common factor in both the terms of the expression. So, take the common factor 3 out.

Now, look at (4y² - 25). They don't have any common factors but they appear in the form of the algebraic identity ⇨ a² - b² = (a + b) (a - b). Here,
- a² = 4, a = 2 (√a² = ✓4 = 2)
- b² = 25, b = 5 (√b² = ✓25 = 5)
So, the (4y² + 25) becomes...

Now, bring the 3 (common factor) & rewrite the complete expression.

We can't further simplify it. Also, remember that the simplified form of an expression is equivalent to the expression. So, 3 (2y - 5) (2y + 5) is equivalent to 12y² - 75.
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