Advertisements
Advertisements
प्रश्न
Answer the following:
Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
उत्तर
`sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2
∴ `sqrt(4log_2x) + (4log_2(sqrt(2/x)))/log_2 4` = 2
∴ `2sqrt(log_2x) + (4 xx 1/2log_2 (2/x))/(2log_2 2)` = 2
∴ `2sqrt(log_2x) + log_2 (2/x)` = 2 ...[∵ log22 = 1]
∴ `2sqrt(log_2x) + log_2 2 - log_2 x` = 2
∴ `2sqrt(log_2 x) + 1 - log_2 x` = 2
∴ `2sqrt(log_2 x)` = 1 + log2x
Squaring both sides, we get,
4 log2x = (1 + log2x)2
∴ 4 log2x = 1 + 2log2x + (log2x)2
∴ (log2x)2 – 2log2x + 1 = 0
∴ (log2x – 1)2 = 0
∴ log2x – 1 = 0
∴ log2x = 1 = log22
∴ x = 2.
APPEARS IN
संबंधित प्रश्न
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
f, g, h are three function defined from R to R as follow:
(ii) g(x) = sin x
Find the range of function.
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(v) \[\frac{g}{f}\]
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
Which one of the following is not a function?
Let f(x) = |x − 1|. Then,
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and} g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\] is equal to
f is a real valued function given by \[f\left( x \right) = 27 x^3 + \frac{1}{x^3}\] and α, β are roots of \[3x + \frac{1}{x} = 12\] . Then,
The domain of definition of \[f\left( x \right) = \sqrt{4x - x^2}\] is
Check if the following relation is a function.
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}
Check if the relation given by the equation represents y as function of x:
x + y2 = 9
Express the area A of circle as a function of its diameter d
An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x3
Express the following exponential equation in logarithmic form
e2 = 7.3890
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Select the correct answer from given alternatives.
Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.
Answer the following:
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b
Answer the following:
Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph
Answer the following:
Simplify `log_10 28/45 - log_10 35/324 + log_10 325/432 - log_10 13/15`
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Answer the following:
Find the range of the following function.
f(x) = |x – 5|
Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Check if this relation is a function
The domain of the function f(x) = `sqrtx` is ______.
The domain of the function f(x) = log3+x (x2 - 1) is ______.
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.
