Question

If `3/2 log a + 2/3` log b - 1 = 0, find the value of a⁹.b⁴ .

Answer 1

`3/2 log a + 2/3` log b - 1 = 0

⇒ `log a^(3/2) + log b^(2/3)` = 1

⇒ log`( a^(3/2) xx b^(2/3)) = 1`

⇒ log`( a^(3/2) xx b^(2/3)) = log 10`

⇒ `( a^(3/2) xx b^(2/3))` = 10

⇒ `( a^(3/2) xx b^(2/3))^6 = 10^6`

⇒ a⁹ . b⁴ = 10⁶