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Log Properties<br />Log properties may seem confusing, but there are many fun ways to manipulate them!<br />
What is a log?<br />A log is a way of rewriting an exponential<br />Logbaseanswer=power<br />23=8<br />Log28=3<br />
Some things about logs<br />If a log has no base written it is assumed the base is ten<br />If a log has a base of e it is...
Logs also have some cool properties<br />Logs that are added, with the same base, can be simplified to one log with their ...
If the expression in your log is raised to a power…<br />You can bring the exponent down as a coefficient!<br />Ln(x+5)6=6...
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Log properties

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Log properties

  1. 1. Log Properties<br />Log properties may seem confusing, but there are many fun ways to manipulate them!<br />
  2. 2. What is a log?<br />A log is a way of rewriting an exponential<br />Logbaseanswer=power<br />23=8<br />Log28=3<br />
  3. 3. Some things about logs<br />If a log has no base written it is assumed the base is ten<br />If a log has a base of e it is written as ln for natural log<br />Since ln is log base e, lne is always 1 and ln1 is always zero<br />
  4. 4. Logs also have some cool properties<br />Logs that are added, with the same base, can be simplified to one log with their expressions multiplied <br />Ln(x+4)+ln(4)=ln(4x+16)<br />Logs that are subtracted, with the same base, can be simplified to one log with their expressions divided (make sure to make the first log’s expression is on the numerator)<br />ln(x+3)-ln(7)=ln((x+3)/7)<br />
  5. 5. If the expression in your log is raised to a power…<br />You can bring the exponent down as a coefficient!<br />Ln(x+5)6=6ln(x+5)<br />But be careful you only bring down the exponent as a coefficient if the quantity inside the log has an exponent, if the entire log is raised to a power you cannot do anything with the exponent<br />

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