\( \log_{x}\left(\frac{9}{16}\right)= -\frac{1}{2}\)

= \( x^{\frac{1}{2}}=\frac{9}{16}\)

= \( \frac{1}{x}=\frac{9}{16}\)

= \( x= \frac{16}{9}\)

= \( x=\left(\frac{16}{9}\right)^{2}\)

= \( x=\frac{256}{81}\)

a^x = b^y

 log a^x = log b^y

 x log a = y log b

\(\frac{\log a}{\log b}=\frac{y}{x}\)

log ₂ x = 10     \(\Rightarrow\)     x = 2¹⁰.

 log_x y = 100

 y = x¹⁰⁰

 y = (2¹⁰)¹⁰⁰     [put value of x]

 y = 2¹⁰⁰⁰.

Let log₂ 16 = n.

Then, 2ⁿ = 16 = 2⁴     \(\Rightarrow
\)     n = 4.

Therefore  log₂ 16 = 4.