Question

Given $\frac{{\log }_{10}16}{{\log }_{10}2}={\log }_{10}a$, find the value of $(a÷100)$.

Answer 1

$\frac{{\log }_{10}16}{{\log }_{10}2}=\frac{{\log }_{10}{2}^4}{{\log }_{10}2}=\frac{4{\log }_{10}2}{{\log }_{10}2}$

$=4$

$4={\log }_{10}a$

$a={10}^4$

$\therefore \therefore a={10}^4=4$

$a÷100=\frac{{10}^4}{{10}^2}$

$=100$