Using Properties of Logarithms

a

To evaluate the common logarithm of a number can be seen as finding what exponent the number

10

must be raised to in order to get that number. Here, we take the logarithm of the number

1000 .

Let's use that we raise

10

to

3

to get the number

1000 .

lo g (1000)

WritePowWrite as a power

lo g (1 0^{3})

lo g (1 0^{m}) = m

3

b

Here we can use the rule we used in Part A directly since the $1 0^{5}$ is already written as a power with the base $10 .$

lo g (1 0^{5})

lo g (1 0^{m}) = m

5

c

What should you raise $10$ to the power of in order for it to equal $1 ?$ Any number, except the number $0,$ raised to the power $0$ equals $1 .$ That means $1$ can be written as $1 0^{0} .$

lo g (1)

WritePowWrite as a power

lo g (1 0^{0})

lo g (1 0^{m}) = m

0

d

To calculate $lo g (\frac{1}{1 0 0}),$ we will rewrite the argument as a power of ten, and then use the same method as previously.

lo g (\frac{1}{1 0 0})

WritePowWrite as a power

lo g (\frac{1}{1 0 ^{2}})

FracToNegExponent

\frac{1}{a ^{m}} = a^{- m}

lo g (1 0^{- 2})

lo g (1 0^{m}) = m

- 2

Using Properties of Logarithms 1.7 - Solution