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Let (x) = 7 + ln(x5) (a) Rewrite (x) using a rule of logarithms so that it does not involve a nested function.

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Final answer:

The function (x) = 7 + ln(x^5) can be simplified into (x) = 7 + 5*ln(x) by applying the power rule of logarithm, which does not involve a nested function. This rule states that the logarithm of a number raised to an exponent is equal to the product of the exponent and the logarithm of the number.

Step-by-step explanation:

This question involves manipulating the composition of logarithmic and exponential functions, and can be solved using properties of logarithms. Given the function (x) = 7 + ln(x5), we can rewrite it using a rule of logarithms called the power rule. The power rule says the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This rule can be written as logb(xn) = n * logb(x), where logb denotes logarithm base b, x the input to the logarithm, and n the exponent to which x is raised. So, applying this rule to the function (x), we get (x) = 7 + 5*ln(x). This new form of the function doesn't involve a nested function, and is easy to work with due to its linearity.

Learn more about Power Rule of Logarithm

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