log_{10}(x-2)+log_{10}(9-x)<1

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

simplify solve for inverse tangent line

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log₁₀(x−2)+log₁₀(9−x)<1

Solution

2<x<4 or 7<x<9

Interval Notation

(2, 4)∪(7, 9)

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Solution steps

One step at a time

log₁₀(x−2)+log₁₀(9−x)<1

Apply log rules

(x−2)(9−x)<10 and (x−2)(9−x)>0

(x−2)(9−x)<10 and (x−2)(9−x)>0 : 2<x<4 or 7<x<9

2<x<4 or 7<x<9

Find positive values for logs: 2<x<9

Combine the intervals

(2<x<4 or 7<x<9) and 2<x<9

Merge Overlapping Intervals

2<x<4 or 7<x<9

Number Line

2<x<4 or 7<x<9

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Notebook

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

log_{10}(x-2)+log_{10}(9-x)<1

Solution

Solution steps

Number Line

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