Use the properties of logarithms and the logarithm property

Use the properties of logarithms and the logarithm property of equality to solve for x. log(lowersubscript)3(x+5)+log(lowersubscript)3(x+4)=log(lowersubscript)3(5x-8)

Solution

Solution: given eq. is log₃(x+5)+log₃(x+4)=log₃(x-8)

from log property x+5>0, x+4>0 & 5x-8>0 conclusion is x>8/5

log₃(x+4)(x+5)=log₃(5x-8)

x²+9x+20=5x-8

x²+4x+28=0

discriminent of this quadretic eq. is negetive, therefore no real value of x

so there is no solution