IXL - Solve logarithmic equations with multiple logarithms (Precalculus practice)

Solve. Simplify your answer.

log

–

log

ref_doc_title.

Learn with an example

question

Solve. Simplify your answer.

log

–

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.

Quotient Property:

log

–

log

where

and

are positive, and

≠

solution

Look at the given equation:

log

–

log

Use the Quotient Property to combine the logarithms.

log

Rewrite this as an exponential equation and solve for

log

140

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

is 140. In other words, the expression inside the logarithm in the original equation must be positive.

log

–

log

140

–

log

Plug in the solution,

140

Plug in the solution,

140

The expressions inside the logarithms are 140 and 14, which are positive. This means the logarithms in the original equation are well defined. So,

140

is a valid solution.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

K.3Solve logarithmic equations with one logarithm

I.4Product property of logarithms

I.5Quotient property of logarithms

B.1Solve linear equations

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