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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

Solutions > Log Power Rule Calculator >

log_{9}(sqrt(3))

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

π

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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simplify log₉(√3)

Solution

14

Decimal

0.25

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Solution steps

One step at a time

log₉(√3)

Factor the number: 9=3²

=log_3²(√3)

Apply log rule: log_a^b(x)=1b log_a(x), a>0

log_3²(√3)=12 log₃(√3)

=12 log₃(√3)

Apply radical rule: √a=a¹²

√3=3¹²

=12 log₃(3¹²)

Apply log rule: log_a(a^b)=b

log₃(3¹²)=12

=12 · 12

12 · 12 =14

=14

Log Power Rule Examples

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