Log properties
- 1. Log PropertiesLog properties may seem confusing, but there are many fun ways to manipulate them!
- 2. What is a log?A log is a way of rewriting an exponentialLogbaseanswer=power23=8Log28=3
- 3. Some things about logsIf a log has no base written it is assumed the base is tenIf a log has a base of e it is written as ln for natural logSince ln is log base e, lne is always 1 and ln1 is always zero
- 4. Logs also have some cool propertiesLogs that are added, with the same base, can be simplified to one log with their expressions multiplied Ln(x+4)+ln(4)=ln(4x+16)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)ln(x+3)-ln(7)=ln((x+3)/7)
- 5. If the expression in your log is raised to a power…You can bring the exponent down as a coefficient!Ln(x+5)6=6ln(x+5)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