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Base expression for log₄ 75 lould be in the form of a fraction.

User YAnTar
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1 Answer

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Final answer:

The base expression for log₄ 75 cannot be written as a simple fraction because 75 is not a power of 4. Instead, using properties of logarithms, it can be written as a sum of simpler logarithmic terms: log₄ 3 + 2 × log₄ 5.

Step-by-step explanation:

The question asks to express the logarithm log₄ 75 as a fraction based on the properties of logarithms. Recalling the property of logarithms that logam - logan corresponds to loga(m/n), we use this to rewrite the logarithm in question.

Since 75 is not a power of 4, we cannot express log₄ 75 as a simple fraction. However, we know that logarithms can be written in terms of other bases. In this case, we can write it as:

log₄ 75 = log₄ (3× 25) = log₄ (3× 52) = log₄ 3 + 2 × log₄ 5

While this is not strictly a fraction, it does express log₄ 75 as a sum of fractions where each part is a logarithm of a simpler number relative to the base 4.

User Olya
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