Find the log at the base

Calculus Level 1

If l o g x 1 8 = − 3 2 log_{x} \dfrac{1}{8}=\dfrac{-3}{2} , then x x is equal to


The answer is 4.

Prathmesh Patil by Prathmesh Patil , 22, India

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2 solutions

Justin Tuazon
Dec 12, 2014

log ⁡ x 1 8 = − 3 2 x − 3 2 = 1 8 1 x x = 1 8 x x = 8 x 3 = 64 x = 4 \log _{ x }{ \frac { 1 }{ 8 } } =\frac { -3 }{ 2 } \\ { x }^{ \frac { -3 }{ 2 } }=\frac { 1 }{ 8 } \\ \frac { 1 }{ x\sqrt { x } } =\frac { 1 }{ 8 } \\ x\sqrt { x } =8\\ { x }^{ 3 }=64\\ x=4

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Ravinder Singh
Dec 4, 2014

log ⁡ x 1 − log ⁡ x 2 3 = − 3 2 \log _{ x }{ 1 } -\log _{ x }{ { 2 }^{ 3 } } =\frac { -3 }{ 2 }\\ log ⁡ x 2 = 1 2 \\\log _{ x }{ 2 } =\frac { 1 }{ 2 } x = 2 x = 4 \sqrt { x } =2\\ x=4

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