Logs!

Helllo,
I hope everyone had a fantastic weekend! :)

1. Logs are another way to write exponents: logbx=a, as an exponent b^a=x
2. To solve a log you write as an exponent.
3. If no base is written for log, it is implied to be 10.
4. The base of ln is always e.
5. If b and x are equal, than they cancel along with the log.

Example 1:
Write the equation in exponential form.
log416=2
4^2=16

Example 2:
Write the equation in exponential form.
log6(1/36)=-2
6^-2=1/36

Example 3:
Write the equation in exponential form.
log101000=3
10^3=1000

Example 4:
Find the logarithm without using a calculator.
a) log100
=log10100=x
10^x=100
x=2
b) log10,000
=log1010,000=x
10^x=10,000
x=4
c) log0.01
log100.01=x
10^x=1/100
x=-2

Example 5:
Find each logarithm without using a calculator.
a) log50.2
3^x=9
3^2=9
x=2
b) log327
3^x=27
x=3
c) log3243
3^x=23
x=5
d) log33^8
3^x=3^8
x=8

Example 6:
Find each logarithm withougt using a calculator.
a) log464
4^x=64
x=3
b) log4(1/64)
4^x=1/64
x=-3
c)log4 fourth root of 4
4^x=fourth root of 4
4^x=4^1/4
x=1/4
d) log 41
4^x=1
x=0