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log_4(30)-log_4(15)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

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∫

ddx

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

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simplify log₄(30)−log₄(15)

Solution

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0.5

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log₄(30)−log₄(15)

Apply log rule: log_a(x) − log_a(y)=log_a(xy )

log₄(30)−log₄(15)=log₄(3015 )

=log₄(3015 )

Factor the number: 4=2²

=log_2²(3015 )

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

log_2²(3015 )=12 log₂(3015 )

=12 log₂(3015 )

Divide the numbers: 3015 =2

=12 log₂(2)

Apply log rule: log_a(a)=1

log₂(2)=1

=12 · 1

Multiply the numbers: 12 · 1=12

=12

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

log_4(30)-log_4(15)

Solution

Solution steps

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