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

Question

10493 views around the world

You can reuse this answer
Creative Commons License

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 $x=3, x=2$ .

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