Advertisements
Advertisements
प्रश्न
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
पर्याय
3
5
2
7
उत्तर
If log (5x – 9) – log (x + 3) = log 2 then x = 5
Explanation:
log (5x – 9) – log (x + 3) = log 2
`therefore (5x - 9)/(x + 3) = 2`
`therefore 3x = 9 + 6`
∴ x = 5
APPEARS IN
संबंधित प्रश्न
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(ii) fg
If f, g and h are real functions defined by
Write the domain and range of function f(x) given by
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
If f(x) = cos (log x), then the value of f(x2) f(y2) −
The range of f(x) = cos [x], for π/2 < x < π/2 is
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(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is
The range of \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is
If f(m) = m2 − 3m + 1, find f(−3)
Which of the following relations are functions? If it is a function determine its domain and range:
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(2)
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x2
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
231 = 23
Express the following logarithmic equation in exponential form
log10 (0.001) = −3
Write the following expression as a single logarithm.
`1/3 log (x - 1) + 1/2 log (x)`
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range
{(12, 1), (3, 1), (5, 2)}
Answer the following:
Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)
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 graph representing the function f(x) is given in it is clear that f(9) = 2
For what value of x is f(x) = 1?
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
A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Write an expression for gf(x) in its simplest form
Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x3 then, find the range of f
If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Find the range of the following functions given by f(x) = 1 + 3 cos2x
(Hint: –1 ≤ cos 2x ≤ 1 ⇒ –3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4)
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)
Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x, and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ______.