Find the domain of the following
f(x)=under root 4^x-(44^x) + 3^x/log_4^(1-x) were _ represents log base and ^ represtent log no
Please answer only those who know how to solve and i dont want any irrelevant ans
the question is of class 12 maths for jee
Answers
Answer:
A useful family of functions that is related to exponential functions is the logarithmic functions. You have been calculating the result of bx, and this gave us the exponential functions. A logarithm is a calculation of the exponent in the equation y = bx. Put another way, finding a logarithm is the same as finding the exponent to which the given base must be raised to get the desired value. The exponent becomes the output rather than the input.
Calculating Exponents
Consider these tables of values using a base of 2.
Table 1
Table 2
Input x, an exponent
Output y
Input x, a number that is a power of 2.
Output y, the exponent of 2.
x
y = 2x
x = 2y
y
−3
−3
−2
−2
−1
−1
0
1
1
0
1
2
2
1
2
4
4
2
3
8
8
3
Note the two tables are the same except the columns are reversed—the point (1, 2) taken from the first table will be the point (2, 1) in the second table.
The graphs of these two relationships should have the same general shape. As shown in the graph, the two curves are symmetrical about the line y = x. Another way to put it, if you rotate the red curve about the line y = x, it will coincide with the blue curve. (This makes sense, because y in the first table becomes x in the second table, and vice versa.)
The equation x = 2y is often written as a logarithmic function (called log function for short). The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logb x is read, “y equals log to the base b of x,” or more simply, “y equals log base b of x.” As with exponential functions, b > 0 and b ≠ 1.
You can see from the graph that the range (y values) of the exponential function (in red) is positive real numbers. Since the input and output have been switched, the domain (x values) of the logarithmic function (in blue) is positive real numbers.
Similarly, the domain of the exponential function (in red) is all real numbers. The range of the logarithmic function (in blue) is all real