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Write the logarithm expression as a single logarithm log₄ 60-log₄ 4+log₄ x =

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Final answer:

To write the given logarithm expression as a single logarithm, we can apply the properties of logarithms. The expression can be simplified as log₄ (15x).

Step-by-step explanation:

To write the given logarithm expression as a single logarithm, we can apply the properties of logarithms.

The first property is that the logarithm of a product is equal to the sum of the logarithms of the individual factors. So, we can rewrite the expression as:

log₄ 60 - log₄ 4 + log₄ x = log₄ (60/4) + log₄ x

The second property is that the logarithm of a fraction is equal to the difference of the logarithms of the numerator and the denominator. Therefore, we can simplify the expression further:

log₄ (60/4) + log₄ x = log₄ (15) + log₄ x

Finally, using the first property again, we can combine the logarithms as:

log₄ (15) + log₄ x = log₄ (15x)

User Akshay Barahate
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