Respuesta :

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: The required value of [tex]\log_{100}75[/tex] is 0.9375.

Step-by-step Explanation: Given that [tex]\log 75=1.875.[/tex]

We are to find the value of the following logarithm :

[tex]log_{100}75.[/tex]

We will be using the following properties of logarithm :

[tex](i)~\log_ba=\dfrac{\log a}{\log b}\\\\\\(ii)~\log a^b=b\log a.[/tex]

Therefore, we have

[tex]\log_{100}75\\\\\\=\dfrac{\log 75}{\log100}\\\\\\=\dfrac{1.875}{\log10^2}\\\\\\=\dfrac{1.875}{2\times\log10}\\\\\\=\dfrac{1.875}{2}~~~~~~~~~~~[since~\log10=1]\\\\\\=0.9375.[/tex]

Thus, the required value of [tex]\log_{100}75[/tex] is 0.9375.

Otras preguntas