Question

If $3^x=4^{x-1}$ then x is equal to

• A. $\frac{2lo{g}_{3}2}{2lo{g}_{3}2-1}$
• B. $\frac{2}{2lo{g}_{2}3}$
• C. $\frac{1}{1-lo{g}_{4}3}$
• D. $\frac{2lo{g}_{2}3}{2lo{g}_{2}3-1}$

Answer 1

Answer: (A), (B), (C)

$3^x=4^{x-1}$
Taking $lo{g}_3$ on both sides, we get
$\Rightarrow xlo{g}_{3}3=(x-1)lo{g}_3^4\Rightarrow x=2lo{g}_{3}2.x-lo{g}_{3}4$
$\Rightarrow x(1-2lo{g}_{3}2)=-2lo{g}_{3}2\Rightarrow x=\frac{2lo{g}_{3}2}{2lo{g}_{3}2-1}$
x = $\frac{1}{1-\frac{1}{2lo{g}_{3}2}}=\frac{1}{1-\frac{1}{lo{g}_{3}4}}=\frac{1}{1-lo{g}_{4}3}=\frac{2}{2-lo{g}_{2}3}$
= $\frac{1}{1-\frac{1}{2}lo{g}_{2}3}=\frac{1}{1-lo{g}_{4}3}$