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

Solve. Round your answer to the nearest thousandth.

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Learn with an example

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 9 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

Divide both sides by

log

Divide both sides by

log

≈

log

≈

0.60206

and

log

≈

0.95424

0.60206

0.95424

log

≈

0.60206

and

log

≈

0.95424

≈

Simplify

0.63093

Simplify

To the nearest thousandth,

≈

0.631

$Confetti$

Excellent!

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Not feeling ready yet? These can help:

CC.2Solve exponential equations using common logarithms

CC.3Solve exponential equations using natural logarithms

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