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