IXL - Evaluate logarithms using properties (Precalculus practice)

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

log

ref_doc_title.

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question

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

log

100

key idea

The logarithm of

with base

is defined as

log

if and only if

where

and

≠

The common logarithm uses base 10. The common logarithm

log

is usually written as

log

without the base.

solution

Look at the given expression.

log

100

Notice that this is a common logarithm with base 10, and

100

can be written as a power of 10. So, use the logarithmic expression to write an exponential equation with base 10, and then solve.

log

100

Let

the value of the logarithm

Let

the value of the logarithm

Convert the logarithmic equation to an exponential equation

100

Convert the logarithmic equation to an exponential equation

100

–

100

–

Set the exponents equal

–

Set the exponents equal

So,

log

100

–

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Work it out

Not feeling ready yet? These can help:

I.4Product property of logarithms

I.5Quotient property of logarithms

I.6Power property of logarithms

I.2Evaluate logarithms

I.3Change of base formula

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