IXL - Solve logarithmic equations II (Algebra 2 practice)

Solve. Simplify your answer.

log

ref_doc_title.

Learn with an example

question

Solve. Simplify your answer.

log

–

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 equation:

log

–

Isolate the logarithm.

log

Rewrite this as an exponential equation and solve for

log

The solution is valid only if the original equation makes sense when

is 10. In other words, the expression inside the logarithm in the original equation must be positive.

log

–

log

–

Plug in the solution,

–

Plug in the solution,

The expression inside the logarithm is 10, which is positive. This means the logarithm in the original equation is well defined. So,

is a valid solution.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

CC.6Solve logarithmic equations I

AA.10Quotient property of logarithms

AA.9Product property of logarithms

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