i have write the equation as a single logarithm

Question

2 lnx-3 lny+1/2 lnz

Answer 1

n * ln ( a ) = ln ( a ^ n )

2 ln ( x ) = ln ( x ^ 2 )

3 ln ( y ) = ln ( y ^ 3 )

( 1 / 2 ) ln ( z ) = ln [ z ^ ( 1 / 2 ) ] = ln [ sqrt ( z) ]

ln ( a ) + ln ( b ) = ln ( a * b )

ln ( a ) - ln ( b ) = ln ( a / b )

In this case:

2 ln ( x ) - 3 ln ( y ) + ( 1 / 2 ) ln ( z ) =

2 ln ( x ) + ( 1 / 2 ) ln ( z ) - 3 ln ( y ) =

ln [ x ^ 2 * sqrt ( z ) / y ^ 3 ]