Advertisements
Advertisements
प्रश्न
Express the following exponential equation in logarithmic form
231 = 23
उत्तर
231 = 23
∴ 1 = log23 23 …[By definition of logarithm]
i.e. log23 23 = 1
APPEARS IN
संबंधित प्रश्न
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.
(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
If \[f\left( x \right) = \frac{x - 1}{x + 1}\] , then show that
(i) \[f\left( \frac{1}{x} \right) = - f\left( x \right)\]
(ii) \[f\left( - \frac{1}{x} \right) = - \frac{1}{f\left( x \right)}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(ii) fg
Let f and g be two functions given by
f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.
Find the domain of f + g
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?
If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is
The range of the function \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\] is
If f : [−2, 2] → R is defined by \[f\left( x \right) = \begin{cases}- 1, & \text{ for } - 2 \leq x \leq 0 \\ x - 1, & \text{ for } 0 \leq x \leq 2\end{cases}\] , then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
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,
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find `f(1/2)`
If f(x) = 3x + a and f(1) = 7 find a and f(4).
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
Express the following exponential equation in logarithmic form
`"e"^(1/2)` = 1.6487
Express the following logarithmic equation in exponential form
log2 64 = 6
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Express the following logarithmic equation in exponential form
log10 (0.001) = −3
Express the following logarithmic equation in exponential form
In `1/2` = – 0.693
Write the following expression as a single logarithm.
`1/3 log (x - 1) + 1/2 log (x)`
Solve for x.
log2 + log(x + 3) – log(3x – 5) = log3
If f(x) = 3x + 5, g(x) = 6x − 1, then find `("f"/"g") (x)` and its domain
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Answer the following:
A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 3
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
Find the domain of the following function.
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
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`
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)
Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
The ratio `(2^(log_2 1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.
