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If (2.3)^x=(0.23)^y=1000 then find the v...

If `(2.3)^x=(0.23)^y=1000` then find the value of `x` and `y`.

Text Solution

Verified by Experts

`(2.3)^x=1000`
Take log on both side
`log_10(2.3)^x=log_10(1000)`
`xlog_10(2.3)=3log_10 10=3`
`x=3/(log2.3)`
`(0.23)^y=1000`
Take log both side
`ylog(0.23)=log1000`
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