Question

If ${\displaystyle \text{log}{x}^2-\text{log}\sqrt{y}}$ = 1, express y in terms of x. Hence find y when x = 2.

Answer 1

${\displaystyle \text{log}{x}^2-\text{log}\sqrt{y}}$ = 1

⇒ ${\displaystyle \text{log}\left(\frac{x^2}{\sqrt{y}}\right)}$ = log 10

⇒ ${\displaystyle \frac{x^2}{\sqrt{y}}}$ = 10

⇒ ${\displaystyle \sqrt{y}=\frac{x^2}{10}}$
Squaring both sides, we get

y = ${\displaystyle {\left(\frac{x^2}{10}\right)}^2=\frac{x^4}{100}}$

Now, when x = 2,
y = ${\displaystyle \frac{2^4}{100}=\frac{16}{100}=\frac{4}{25}}$.