Advertisements
Advertisements
Question
Solution
log3 [log2 (log3x)] = 1
∴ log2 (log3x) = 31 = 3
∴ log3x = 23 = 8
∴ x = 38 = 6561.
APPEARS IN
RELATED QUESTIONS
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
- {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
- {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
- {(1, 3), (1, 5), (2, 5)}
f, g, h are three function defined from R to R as follow:
(i) f(x) = x2
Find the range of function.
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(b) f2 = {(1, 1), (2, 7), (3, 5)}
If f(x) = (x − a)2 (x − b)2, find f(a + b).
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:
(vi) \[2f - \sqrt{5} g\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
Write the range of the function f(x) = ex−[x], x ∈ R.
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
The domain of definition of \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
Which of the following relations are functions? If it is a function determine its domain and range:
{(0, 0), (1, 1), (1, −1), (4, 2), (4, −2), (9, 3), (9, −3), (16, 4), (16, −4)}
If f(x) = 3x + a and f(1) = 7 find a and f(4).
Check if the following relation is a function.
Express the area A of circle as a function of its circumference C.
Express the following logarithmic equation in exponential form
ln 1 = 0
Express the following logarithmic equation in exponential form
ln e = 1
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b
Solve for x.
2 log10 x = `1 + log_10 (x + 11/10)`
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
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 domain of the following function.
f(x) = `(x^2 + 4x + 4)/(x^2 + x - 6)`
A graph representing the function f(x) is given in it is clear that f(9) = 2
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
A function f is defined by f(x) = 2x – 3 find x such that f(x) = x
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 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 |
Find a and b
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 |
Find the length of forehand of a person if the height is 53.3 inches
A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
The domain of the function f(x) = `sin^-1((|x| + 5)/(x^2 + 1))` is (–∞, –a] ≈ [a, ∞). Then a is equal to ______.
The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.