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

Solutions > Log Product Rule Calculator >

log_{2}(2x)

Topic

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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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Steps Examples

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simplify log₂(2x)

Solution

1+log₂(x)

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Solution steps

One step at a time

log₂(2x)

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

log₂(2x)=log₂(2)+log₂(x)

=log₂(2)+log₂(x)

Apply log rule: log_a(a)=1

log₂(2)=1

=1+log₂(x)

Solve instead

f(x)=log₂(2x)

ddx (log₂(2x))

Log Product Rule Examples

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