IXL - Solve exponential equations using common logarithms (Algebra 2 practice)

Solve. Round your answer to the nearest thousandth.

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question

Solve. Round your answer to the nearest thousandth.

key idea

Power Property:

log

where

and

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 given equation:

Notice that 5 and 4 cannot be easily written in terms of the same base. So, take the common logarithm (log) of both sides and solve for

log

Take the common logarithm (log) of both sides

log

Take the common logarithm (log) of both sides

log

Power Property

log

Power Property

log

Divide both sides by

log

Divide both sides by

log

0.69897

0.60206

≈

log

≈

0.69897

and

log

≈

0.60206

log

≈

0.69897

and

log

≈

0.60206

1.16096

≈

Simplify

To the nearest thousandth,

≈

1.161

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Work it out

Not feeling ready yet? These can help:

AA.11Power property of logarithms

C.8Solve two-step linear equations

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