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

Solutions > Logarithmic Inequalities Calculator >

2^{log_2(8x-5)}<= 6

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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2^{log₂(8x−5)}≤ 6

Solution

58 <x≤118

Interval Notation

(58 , 118 ]

Decimal

0.625<x≤ 1.375

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Solution steps

One step at a time

2^{log₂(8x−5)}≤ 6

Apply log rules

8x−5≤ 6

8x−5≤ 6 : x≤ 118

x≤ 118

Find positive values for logs: x>58

Combine the intervals

x≤ 118 and x>58

Merge Overlapping Intervals

58 <x≤ 118

Number Line

58 <x≤ 118

Logarithmic Inequalities Examples

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