Question

ln(3x+5)-ln(4)=ln(x-1)

Answer 1

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

ln ( 3 x + 5 ) - ln ( 4 ) = ln [ ( 3 x + 5 ) / 4 ]

ln ( 3 x + 5 )- ln ( 4 ) = ln [ ( 3 x + 5 ) / 4 ] = ln ( x + 1 )

Cancel logarithms by taking exp of both sides

( 3 x + 5 ) / 4 = x - 1 Multiply both sides by 4

3 x + 5 = 4 * ( x - 1 )

3 x + 5 = 4 x - 4

3x - 4 x = - 4 - 5

- x = - 9 Multiply both sides by - 1

x = 9