Question

If 2 log a + 3 log b=2 then prove that a square× b cube=100​

Answer 1

Hey Buddy

Here's The Answer

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Given :-

2 log a + 3 log b = 2

To Prove :-

a² × b³ = 100

Now, we know => x log y = log yˣ

Using the same property

=> 2 log a + 3 log b = 2

=> log a² + log b³ = 2

Now, we also know => log a + log b = log ( a × b )

Using the above property

=> log a² + log b³ = 2

=> log ( a² × b³ ) = 2

We can also write it as

=> log ( a² × b³ ) = 2 × 1

We know, log 10 = 1 , so we can replace 1 by log 10

=> log ( a² × b³ ) = 2 × 1

=> log ( a² × b³ ) = 2 × log 10

=> log ( a² × b³ ) = log 10²

Cancelling logs both side

=> ( a² × b³ ) = 10²

=> ( a² × b³ ) = 100

Hence Proved.

Hope It Helps.

Answer 2

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