Logarithm Questions - Solve Now!

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Homework Help Overview

The discussion revolves around simplifying logarithmic expressions, specifically focusing on the equation involving logarithms with a base of \(3a\) and the number \(9\). Participants are exploring the application of logarithmic properties to rewrite the expression correctly.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • One participant attempts to simplify the logarithmic expression using known properties, while another emphasizes the importance of applying the fundamental principle of logarithms. There are questions about the correct application of these principles and the format of mathematical expressions shared in the thread.

Discussion Status

The discussion is ongoing, with participants providing guidance on the application of logarithmic rules and the proper formatting of mathematical expressions. There is no explicit consensus yet, but there are suggestions for improvement in understanding and presentation.

Contextual Notes

One participant notes that this is part of a series of threads on logarithms, indicating a potential pattern in the original poster's approach to the topic. There is also a mention of a preference for LaTeX formatting for mathematical expressions.

Jouster
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Homework Statement
By changing the base of log[SUB]3a[/SUB]9, express (log3a9)(1+loga3) as a single logarithm to base a. I don't know what to do to simplify the equation further
Relevant Equations
Logarithms
1671093569418.png
 
Last edited:
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Jouster said:
I don't know what to do to simplify the equation further
Minimize your algebra by applying what you know about logarithms to finish rewriting your first line:
$$\log_{3a}9=\frac{\log_{a}9}{\log_{a}3a}=\frac{\log_{a}3^{2}}{\log_{a}a+\log_{a}3}=\frac{2\log_{a}3}{1+\log_{a}3}$$
 
@Jouster: this is the latest of several threads you've started about logarithms where you have not applied the fundamental principle of logarithms: \log_a(bc) = \log_a(b) + \log_a(c). You need to get into the habit of applying this principle before asking for help.
 
Also @Jouster -- Please post your math using LaTeX, not in images. See the "LaTeX Guide" link below the Edit window for more information. Thank you.
 

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