a. Evaluate loga 120 by computing (log120)/(log8) to four decimal places. b. Evaluate log8 120 b

step 1 So in the given question we are told to evaluate a logarithmic expression that is given as log w

A. Evaluate loga 120 by computing (log120)/(log8) to four...

a. Evaluate $\log _{a} 120$ by computing $\frac{\log 120}{\log 8}$ to four decimal places.
b. Evaluate $\log _{8} 120$ by computing $\frac{\ln 120}{\ln 8}$ to four decimal places.
c. How do your answers to parts ( a ) and (b) compare?

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Key Concepts

Decimal Approximation

Decimal approximation refers to the process of representing a computed value as a decimal number up to a specified number of decimal places. This technique is crucial when obtaining numerical estimates for logarithmic values and ensuring consistency across computations, especially in applied mathematics and scientific calculations.

Change-of-Base Formula

This formula allows you to compute logarithms in any base by using logarithms in a different base. Its general form, log_b x = (log_k x) / (log_k b), is essential because most calculators only support logarithms with specific bases, typically 10 or e. It also shows that regardless of the logarithm base used for the computation, the value remains the same.

Logarithm

A logarithm is the inverse operation to exponentiation and answers the question, 'to what power must a base be raised to produce a given number?' It is a fundamental concept in mathematics that is used to solve exponential equations and to describe phenomena that change multiplicatively.

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