Express the following logarithms in terms of ln5 and ln7 . a. ln(1 / 125) b. ln9.8 c. ln7 √(7) d

step 1 All right, so for this problem, we're going to express the following logarithms in terms of LN o

Express the following logarithms in terms of ln5 and ln7 ....

Key Concepts

Logarithm Properties

This concept covers the foundational rules of logarithms, including the product, quotient, and power rules. These rules allow complex logarithmic expressions to be broken down and rewritten as sums, differences, or multiples of simpler logarithms, making it easier to manipulate and simplify the expressions.

Power Rule for Logarithms

The power rule states that the logarithm of a number raised to an exponent is equal to that exponent multiplied by the logarithm of the number. This is especially useful when dealing with exponential expressions or radicals, as it enables the conversion of powers into multiplicative factors.

Product Rule for Logarithms

The product rule indicates that the logarithm of a product of two or more numbers is equal to the sum of the logarithms of the individual factors. This rule simplifies expressions where multiplication is involved by breaking them into additive components.

Quotient Rule for Logarithms

The quotient rule expresses the logarithm of a quotient as the difference between the logarithm of the numerator and the logarithm of the denominator. This rule is vital for simplifying expressions that involve division.

Representation of Numbers in Terms of Prime Factors

This concept involves rewriting composite numbers as powers of their prime factors. It enables the expression of logarithms of composite numbers in terms of logarithms of primes, which is crucial when a logarithmic expression needs to be written in terms of specific logarithms like ln 5 and ln 7.

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