Logarithms

A logarithm is just another form of an exponent.

$2^3=8lo{g}_{2}8=3$

The logarithm tells you what the exponent is:


How to do log calculations without calculator.

If you have an unknown value in log form, you first change the equation to exponential form and then solve the unknown value.

$x=lo{g}_{5}2525=5^x{5}^2=5^x\therefore <!--\; \therefore \; -->x=2$

Logs, antilog, log_e and antilog_e a calculator.

Use your calculator '2ndF log' to get antilog and '2ndF IN' to obtain log_e


Log Laws


Law 1

If the base and number are the same the log cancels out and the answer is 1.

log_aa 

= 1

Law 
If you have two logs and their bases are the same, you multiply the numbers.

log_ca + log_cb

= log_cab

Law 3
If you have two logs with the same base and you are subtracting, you divide the numbers.

log_ca - log_cb

= log_c^a/_b

Law 4
If you have a base, number and exponent you write the exponent in front of the log.

log_ab^m

= m log_ab

Law 5
If you have a log with a different base and number you can change the base.

$lo{g}_{a}b=\frac{lo{g}_{c}b}{lo{g}_{c}a}$

Simplify logs without a calculator




Changing the base of a log