Logs have many useful properties that allow them to be simplified. Logs with the same base can have their expressions combined by multiplying or dividing the expressions, depending on if they are added or subtracted. Additionally, if the expression inside a log is raised to a power, the exponent can be brought down as a coefficient to the outside of the log. However, exponents only apply to the expression inside the log, not the log as a whole.

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