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Example 10.36: Condensing a Logarithm Using the Power Property
To condense a logarithmic expression that includes coefficients, such as , start by applying the Power Property in reverse, , to move the coefficients inside the logarithms as exponents. This yields . Once the coefficients are removed, use the Product Property to combine the added logarithms into a single logarithm. The final condensed expression is .
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Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
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Example 10.35: Condensing a Logarithm with Multiple Terms
Example 10.36: Condensing a Logarithm Using the Power Property
Solving Logarithmic Equations by Condensing
A technician is condensing a logarithmic expression to simplify a formula. To prepare the terms for combination, they must first move any coefficients back as exponents (for example, rewriting as ). Which property of logarithms should they recall to perform this step?
A sound technician is measuring audio intensity levels across different recording channels. To simplify the data for a report, they need to condense a formula containing multiple logarithmic decibel readings into a single term. Match each logarithmic property to the correct role it plays in the condensing process.
A logistics coordinator is simplifying a formula used to calculate fuel efficiency across different shipping routes. The formula contains several expanded logarithmic terms that need to be condensed into a single expression for a summary report. Arrange the following steps in the correct order to successfully condense the logarithmic expression.
A database administrator is optimizing a performance-tracking query that involves two logarithmic terms with different bases: and . True or False: These two terms can be condensed into a single logarithm using the Product Property.
A geologist is simplifying a seismic activity formula that involves the difference between two logarithmic terms with the same base: . To condense this subtraction into the single term , the geologist must apply the ____ Property of Logarithms.
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In technical fields like data science or engineering, simplifying mathematical models is essential for efficiency. According to the Power Property of Logarithms (), what is the correct first step when condensing the expression ?
As an environmental data analyst modeling population growth, you must condense the logarithmic equation to simplify your forecasting software. You recall that your very first step is to move the coefficients 2 and 3 inside their respective logarithms as exponents by applying the _____ Property in reverse.
A telecommunications technician is optimizing a signal strength model by condensing the expression into a single logarithm. Match each logarithmic property to the specific role it plays in this two-step simplification process.
A data analyst is simplifying a growth model to be used in a financial forecasting tool. To condense the expression into a single logarithm, in what order should the following steps be performed according to the properties of logarithms?
An acoustics engineer is simplifying a sound intensity model that contains the expression . True or False: According to the Power Property of Logarithms, the first step in condensing this expression is to move the coefficients 2 and 4 to the exponent position, resulting in .