Question

if 2x= 3y=48z find x in terms of y and z. plz solve it asap its urgent

Answer 1

Here is your solution :

Given,

=> 2^x = 3^y = 48^z

Let, 2^x = k

So,

=> 2^x = 3^y = 48^z = k

Now,

=> 2^x = k

•°• 2 = k^( 1/x )

And,

=> 3^y = k

•°• 3 = k^( 1/y )

And,

=> 48^z = k

=> 48 = k^( 1/z )

=> ( 2 × 2 × 2 × 2 × 3 ) = k^( 1/z )

=> ( 2⁴ × 3 ) = k^( 1/z )

Substitute the value of 2 and 3,

=> [ { k^( 1/x ) }⁴ × k^( 1/y ) ] = k^z

Using identity,

=> [ { a^( 1/m ) }^n = a^( n/m ) ]


=> [ { k^( 4/x ) } × k^( 1/y ) ] = k^z

Using identity,

=> [ a^m × a^n = a^( m + n ) ]


=> k^{ ( 4/x ) + ( 1/y ) } = k^z

=> k^{ ( 4y + x ) / xy } = k^z

As bases are equal,so exponent will be also equal.

=> ( 4y + x ) / xy = z

=> ( 4y + x ) = xyz

=> 4y + x = xyz

=> 4y = xyz - x

=> 4y = x( yz - 1 )

=> 4y/( yz - 1 ) = x

•°• x = 4y / ( yz - 1 )