If $ 3^x = 4^{ x - 1} $ then x is equal to
- $ \frac{ 2 \, log_3 \, 2}{ 2 log_3 2 - 1}$
- $ \frac{ 2}{ 2 log_2 3 }$
- $ \frac{ 1}{ 1 - log_4 3 } $
- $ \frac{ 2 log_2 \, 3} { 2 log_2 3 - 1}$
The Correct Option is C
Solution and Explanation
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Concepts Used:
Exponential and Logarithmic Functions
Logarithmic Functions:
The inverses of exponential functions are the logarithmic functions. The exponential function is y = ax and its inverse is x = ay. The logarithmic function y = logax is derived as the equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, (where, a > 0, and a≠1). In totality, it is called the logarithmic function with base a.
The domain of a logarithmic function is real numbers greater than 0, and the range is real numbers. The graph of y = logax is symmetrical to the graph of y = ax w.r.t. the line y = x. This relationship is true for any of the exponential functions and their inverse.
Exponential Functions:
Exponential functions have the formation as:
f(x)=bx
where,
b = the base
x = the exponent (or power)