Question

# If ( log (5-x)-frac{1}{3} log left(35-x^{3}right)=0 ) then the values of ( x ) are

Solution

( quad log (5-x)-frac{1}{3} log left(35-x^{3}right)=0 quad Rightarrow quad 3 log (5-x)=log left(35-x^{3}right) )

( Rightarrow quad(5-x)^{3}=35-x^{3} Rightarrow 125-x^{3}-32+5 x-75 x^{2}= 35-x^{3})

( begin{array}{rl}Rightarrow quad 15 x^{2}+75 x+125-35=0 & =15 x^{2}+75 x+90=0 Rightarrow quad x^{2}+5 x+6=0 & Rightarrow quad & x(x+2)(x+3)=0 Rightarrow quad x= & -2,-3end{array} )