how can I get the Value of an exponent ?
Examples 3^x= 2187*81

Question

how can I get the Value of an exponent  ? 
Examples 3^x= 2187*81

ganeshie8 · Answer

see if 2187 can be written as powers of 3

akashdeepdeb · Answer

3^x = 2187*81

Now break up the RHS in the form of exponents with base 3

3^x = 243*9*81
3^x = 3^5 * 3^2 * 3^4

$$3^x = 3^{5+2+4}$$ [Basic laws of exponents]

So

$$3^x = 3^{11}$$

Now if the bases are same ie. 3 then even their powers have to be the same.

Understood? :)

akashdeepdeb · Answer

@EinsteinMorse ?

anonymous · Answer

Yeah thanks . Can you give some sort of examples?

anonymous · Answer

You need two identities to solve this:
$$x ^{n} = n*\log(x)$$ and $$a*b = \log(a) + \log(b)$$

Take into consideration the info AkashdeepDeb provided, and it becomes straight forward algebra. (working on detailed steps...)