# If #3^m = 2 and 4^n =27#, show by laws of indices that #m xx n =3/2#??

##### 3 Answers

see a solution process below;

#### Explanation:

Note, we can also use Law or Logarithm to solve this;

Log both sides..

similarly..

Log both sides..

Hence;

As required!

#### Explanation:

#4^n=(2^2)^n=(2)^(2n)=27=3^3larr"from "4^n=27#

#"substitute "2=3^m#

#rArr(3^m)^(2n)=3^3#

#rArr3^(2mn)=3^3#

#"since bases on both sides are 3, equate the exponents"#

#rArr2mn=3#

#rArrmn=3/2#

See below.

#### Explanation:

We have

We can write that as:

Since

Since the bases are equal, the exponents are equal too.

Proved.