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Question
Find the value of x in the following:
`(3/5)^x(5/3)^(2x)=125/27`
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Solution
Given `(3/5)^x(5/3)^(2x)=125/27`
`3^x/5^x xx5^(2x)/3^(2x)=125/27`
`3^x/3^(2x)xx5^(2x)/5^x=125/27`
`5^(2x-x)/3^(2x-x)=125/27`
`5^(2x-x)/3^(2x-x)=5^3/3^3`
`(5/3)^(2x-x)=(5/3)^3`
Comparing exponents we get
2x - x = 3
x = 3
Hence, the value of x = 3.
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