Solve Logarithms with Ease: 2log10 + log10(1/2 + 1/3) + 1/3log27 Explained

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SUMMARY

The discussion focuses on evaluating the expression 2log10 + log10(1/2 + 1/3) + 1/3log27. The user initially miscalculated log10(1/2 + 1/3) but corrected it to log10(5/6) after realizing that log(a + b) does not equal log(a) + log(b). The final evaluation led to the correct result of 1. The key takeaway is the importance of correctly applying logarithmic properties in calculations.

PREREQUISITES
  • Understanding of logarithmic properties, specifically log(a + b) ≠ log(a) + log(b)
  • Familiarity with base-10 logarithms (log10)
  • Basic arithmetic operations involving fractions
  • Knowledge of logarithmic identities, such as the change of base formula
NEXT STEPS
  • Study logarithmic properties in depth, focusing on addition and multiplication rules
  • Practice evaluating logarithmic expressions with different bases, including natural logarithms
  • Explore logarithmic equations and their applications in real-world scenarios
  • Learn about the change of base formula for logarithms and its practical uses
USEFUL FOR

Students, educators, and anyone seeking to improve their understanding of logarithmic functions and their applications in mathematics.

lionely
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Without using tables:

1. Evaluate 2log10 + log10(1/2 + 1/3) + 1/3log27

2log2 + log 1 - log2 + log1 - log3 + log3 = log2..

This was my attempt but it's wrong . I think I went wrong somewhere here log10(1/2 + 1/3) but I can't find the error.
 
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lionely said:
Without using tables:

1. Evaluate 2log102 + log10(1/2 + 1/3) + 1/3log27

2log2 + log 1 - log2 + log1 - log3 + log3 = log2..

This was my attempt but it's wrong . I think I went wrong somewhere here log10(1/2 + 1/3) but I can't find the error.
log(a + b) ≠ log(a) + log(b)


What is (1/2) + (1/3) ?
 
oh so it should be log(5/6) ?
 
Oh yes I got it! I got 1. Thanks for pointing that out.
 

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