Question

If $\log _b a=3, \log _b c=-4$ 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

• A. irrational
• B. rational
• C. prime
• D. composite

Answer 1

Answer: (B), (D)

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