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If log(10) 4 = 0.6021 and log(10)5 = 0.6...

If `log_(10)` 4 = 0.6021 and `log_(10)5` = 0.6990, then find the value of `log_(10)` 1600.

Text Solution

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`log_(10)1600=log_(10)(64xx25)=log_(10)(4^(3)xx5^(2))`
`=log_(10)4^(3)+log_(10)5^(2)`
`=3log_(10)4+2log_(10)5`
`=3(0.6021)+2(0.6990)`
=1.8063 + 1.3980
`log_(10)` 1600 = 3.2043.
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