Logs

You can write a log as an exponent, and an exponent as a log.

logb(x) = a then, b^a=x

(b will be a subscript)

To solve a log you write as an exponent.

If no base is written for log, it is implied to be 10.

The base of ln is always e, and is worked the exact same as log.

If b and x are equal, than they cancel along with the log.

Ex 1:

Write the equation in exponential form.

log6(1/36)=-2

6^-2=1/36

Ex 2:

Write the equation in exponential form.

log4(16)=2

4^2=16

Ex 3:

Find each logarithm without using a calculator.

log3(27)

3^x=27

x=3

Ex 4.

Find each logarithm withougt using a calculator.

log4(64)

4^x=64

x=3

Ex 5:

Find the logarithm without using a calculator.

log10,000

10^x=10,000

x=4