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

☐²

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ddx

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

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1<e^3x−1<2

Solution

13 <x<ln(2)+13

Interval Notation

(13 , ln(2)+13 )

Decimal

0.33333…<x<0.56438…

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Solution steps

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1<e^3x−1<2

If a<u<b then a<u and u<b

1<e^3x−1 and e^3x−1<2

1<e^3x−1 : x>13

e^3x−1<2 : x<ln(2)+13

Combine the intervals

x>13 and x<ln(2)+13

Merge Overlapping Intervals

13 <x<ln(2)+13

Number Line

13 <x<ln(2)+13

Exponential Inequalities Examples

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Notebook

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

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