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Let n=75600, then find the value of 4/(l...

Let `n=75600`, then find the value of `4/(log_2 n)+3/(log_3 n)+2/(log_5 n)+1/(log_7 n)`.

Text Solution

Verified by Experts

`log_ax = 1/log_xa`
So, our expression becomes,
`4log_n2+3log_n3+2log_n5+log_n7`
`=log_n(2^4)+log_n(3^3)+log_n(5^2)+log_n7`
`=log_n16+log_n27+log_n25+log_n7`
`=log_n(16**25**25**7)`(As `log_na+log_nb = log_n(ab)`)
`=log_n(75600)`
As, `n = 75600`
...
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