IXL - Change of base formula (Algebra 2 practice)

Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

log

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question

Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

log

key idea

The Change of Base Formula can be used to change a logarithm from base

to base

log

where all numbers are positive,

≠

and

≠

A common logarithm uses base 10. The common logarithm

log

is usually written as

log

without the base.

solution

Look at the Change of Base Formula:

log

Now figure out the values of

and

The problem gives the logarithm

log

It is of the form

log

with

and

The problem asks for the given logarithm to be rewritten using common logarithms. This means

log

will be

log

which is usually rewritten as log.

Finally, complete the change of base formula.

log

Change of Base Formula

log

Change of Base Formula

Plug in

and

log

Plug in

and

Rewrite

log

as log

log

Rewrite

log

as log

So,

log

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AA.3Convert between exponential and logarithmic form: all bases

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