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)