How do you solve #(log(35 - x^3))/( log( 5 - x ))=3#?

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Answer 1 · 2016-07-17T17:13:18

The soln. is #x=3, x=2#.

We will use these Rules :

#(R1) : mloga=loga^m#

#(R2) : (a-b)^3=a^3-b^3-3ab(a-b)#

Now, given that, #log(35-x^3)/log(5-x)=3#

#:. log(35-x^3)=3log(5-x)=log(5-x)^3#

Since log is #1-1# fun., we get, #35-x^3=(5-x)^3#

#:. 35-x^3=125-x^3-3*5*x(5-x)#

#=125-x^3-75x+15x^2#

#:. 15x^2-75x+90=0#

#:. x^2-5x+6=0#

#:. (x-3)(x-2)=0#

The soln. is #x=3, x=2#.