math solving for x?

Question

solve for x. show steps
a) 3.4x to the exponent 2.5= 24.3 to the exponent 3.4

b) 3(x-2)squared = (3x-2)(x+5)

Answer 1

( 3.4 x )^2.5 = ( 24.3 )^3.4

Take the natural log of both sides...

( 2.5 ) ln ( 3.4 x ) = ( 3.4 ) ln ( 24.3 )

ln ( 3.4 x ) = ( 3.4 ) ln ( 24.3 ) / ( 2.5 )

Rule of logs: log ( ab ) = log ( a ) + log ( b )

ln ( 3.4 ) + ln ( x ) = ( 3.4 ) ln ( 24.3 ) / ( 2.5 )

ln ( x ) = ( 3.4 ) ln ( 24.3 ) / ( 2.5 ) - ln ( 3.4 )

Take the inverse natural log of both sides...

x = e^[ ( 3.4 ) ln ( 24.3 ) / ( 2.5 ) - ln ( 3.4 ) ]

The second is done in a similar fashion.