Question

If log75=1.875

then what is the value of log (sub 100) 75?

Answer 1

log(sub100)X = Y, means 100^Y = X, 100^Y = (10^2)^Y = 10^2Y,

so ... log(sub100) X = logX /2!

and log(sub100)75 = 1.875/2 = 0.9375

Answer 2

Answer: The required value of
`\log_(100)75` is 0.9375.

Step-by-step Explanation: Given that
`\log 75=1.875.`

We are to find the value of the following logarithm :

`log_(100)75.`

We will be using the following properties of logarithm :

`(i)~\log_ba=(\log a)/(\log b)\\\\\\(ii)~\log a^b=b\log a.`

Therefore, we have

`\log_(100)75\\\\\\=(\log 75)/(\log100)\\\\\\=(1.875)/(\log10^2)\\\\\\=(1.875)/(2*\log10)\\\\\\=(1.875)/(2)~~~~~~~~~~~[since~\log10=1]\\\\\\=0.9375.`

Thus, the required value of
`\log_(100)75` is 0.9375.