If log b a=3, log b c=-4 and if the value of x satisfying the equation a3 x=cx-1 is expressed in the form p/q, where p and q are relatively prime then p + q is

Question

If log b a=3, log b c=-4 and if the value of x satisfying the equation a3 x=cx-1 is expressed in the form p/q, where p and q are relatively prime then p + q is (A) irrational (B) rational (C) prime (D) composite

Tardigrade Admin · Accepted Answer

Given log b a =3, log b c =-4 Given, a3 x=cx-1 3 x log b a =( x -1) log b c 3 x × 3=-4(x-1) ⇒ 9 x=4-4 x ⇒ x=4 / 13

Q. If $lo g_{b} a = 3, lo g_{b} c = - 4$ and if the value of $x$ satisfying the equation $a^{3 x} = c^{x - 1}$ is expressed in the form p/q, where p and q are relatively prime then p + q is

irrational

rational

prime

composite

Given $lo g_{b} a = 3, lo g_{b} c = - 4$
Given, $a^{3 x} = c^{x - 1}$
$3 x lo g_{b} a = (x - 1) lo g_{b} c$
$3 x \times 3 = - 4 (x - 1) \Rightarrow 9 x = 4 - 4 x \Rightarrow x = 4/13$

Q. If logb​a=3,logb​c=−4 and if the value of x satisfying the equation a3x=cx−1 is expressed in the form p/q, where p and q are relatively prime then p + q is