Question

write the expression log (sub 2) 7 - log (sub 2) 9 + 2log (sub 2) x as a single algorithm

Answer 1

\[log_2(7)-log_2(9)+2log_2(x)\]

So we need to know three Logarithm rules:

\(log_a(x)+log_a(y)=log_a(xy)\)
\(log_a(x)-log_a(y)=log_a\left(\frac{x}{y}\right)\)
\(y \phantom{.} log_a(x)=log_a(x^y)\)

So we can proceed:
\(log_2(7)-log_2(9)+2log_2(x)\)
\(=log_2\left(\frac{7}{9}\right)+log_2(x^2)\)
\(=log_2\left(\frac{7x^2}{9}\right)\)

Answer 2

ty

Answer 3

np