Rewriting expression of logarithm

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SUMMARY

The discussion focuses on rewriting the logarithmic expression log55x2 as a sum of logarithms. The correct transformation involves using the properties of logarithms, specifically log(a*b) = log(a) + log(b). The final expression is simplified to 1 + 2log5x, confirming the application of logarithmic rules. Participants emphasized the importance of understanding logarithmic identities for accurate manipulation of expressions.

PREREQUISITES
  • Understanding of logarithmic properties, specifically log(a*b) = log(a) + log(b).
  • Familiarity with the concept of rewriting expressions in mathematics.
  • Basic algebra skills for manipulating mathematical expressions.
  • Knowledge of logarithmic notation and terminology.
NEXT STEPS
  • Study the properties of logarithms in detail, including change of base and product rules.
  • Practice rewriting complex logarithmic expressions using various identities.
  • Explore advanced logarithmic applications in calculus and exponential functions.
  • Learn about common logarithmic equations and their solutions in algebra.
USEFUL FOR

Students studying algebra, mathematics educators, and anyone looking to strengthen their understanding of logarithmic expressions and properties.

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Homework Statement


Rewrite the expression as a sum, difference or multiple of logs.

log55x2

Homework Equations





The Attempt at a Solution



log55x2 =
2log55x =
...
 
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That's not the right first, step. What do you know about the addition of logs? If that doesn't help, substitute a = 5 and b = x2 and re-ask my question.

The Bob
 
ooh~
log55 + log5x2 =
1+log5x2 =
1 + 2log5x2!
thank you so much
 
Make that 1 + 2log5x and you're there.
 

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