Know the identities

Algebra Level 2

2 log ⁡ 125 x = log ⁡ 5 9 \boldsymbol {2\log_{125}x= \log_{5}9}

Find the value of x \boldsymbol {x} in the equation above.


The answer is 27.

Md Omur Faruque by MD Omur Faruque , 25, Bangladesh

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1 solution

Kay Xspre
Aug 5, 2015

Simplify the equation gives 2 l o g 5 3 x = l o g 5 3 2 2log_{5^{3}}{x} = log_{5}{3^{2}} or: 2 3 l o g 5 x = 2 l o g 5 3 \frac{2}{3}log_{5}{x} = 2log_{5}{3}

From l o g 5 x 3 = l o g 5 3 log_{5}{\sqrt[3]{x}} = log_{5}{3} it will gives x 3 = 3 \sqrt[3]{x} = 3 or x = 27 x=27

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