Logarithm Questions - Solve Now!

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SUMMARY

The discussion centers on simplifying logarithmic equations, specifically the expression $$\log_{3a}9$$. The correct simplification involves using the change of base formula and the properties of logarithms, resulting in $$\frac{2\log_{a}3}{1+\log_{a}3}$$. Participants emphasize the importance of applying the fundamental principle of logarithms, particularly $$\log_a(bc) = \log_a(b) + \log_a(c)$$, to avoid confusion in future problems. Additionally, contributors request that mathematical expressions be formatted using LaTeX for clarity.

PREREQUISITES
  • Understanding of logarithmic properties, including the change of base formula.
  • Familiarity with LaTeX for mathematical notation.
  • Basic algebra skills for manipulating equations.
  • Knowledge of the fundamental principle of logarithms: $$\log_a(bc) = \log_a(b) + \log_a(c)$$.
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  • Study the change of base formula for logarithms in depth.
  • Practice simplifying logarithmic expressions using LaTeX.
  • Explore advanced logarithmic identities and their applications.
  • Review algebraic techniques for solving logarithmic equations.
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Students learning algebra, educators teaching logarithmic concepts, and anyone looking to improve their skills in simplifying logarithmic expressions.

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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
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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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