Question

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

• A. $ \frac{ 2 \, log_3 \, 2}{ 2 log_3 2 - 1}$
• B. $ \frac{ 2}{ 2 log_2 3 }$
• C. $ \frac{ 1}{ 1 - log_4 3 } $
• D. $ \frac{ 2 log_2 \, 3} { 2 log_2 3 - 1}$

Answer 1

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

$ 3^x = 4^{ x - 1} $
Taking $log_3$ on both sides, we get
$\Rightarrow x \, log_3 3 = (x - 1) log_3^4 \Rightarrow x = 2 log_3 2 . x - log_3 4 $
$\Rightarrow x ( 1 - 2 \, log_3 \, 2) = - 2 \, log_3 2 \Rightarrow x = \frac{ 2 log_3 2 }{ 2 log_3 2 - 1} $
x = $ \frac{1}{ 1 - \frac{1}{ 2 log_3 2 } } = \frac{1}{ 1 - \frac{1}{ log_3 4 } } = \frac{1}{ 1 - log_4 3 } = \frac{2}{ 2 - log_2 3} $
= $ \frac{1}{ 1 - \frac{1}{2} log_2 3 } = \frac{1}{ 1 - log_4 3 }$