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
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.
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) = (a − xn)1/n, a > 0 and n ∈ N, then prove that f(f(x)) = x for all x.
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
If f, g and h are real functions defined by
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
Write the range of the function f(x) = ex−[x], x ∈ R.
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 : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
Which of the following are functions?
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} =
The range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
Let \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?
Check if the following relation is function:
A function f is defined as follows: f(x) = 4x + 5, for −4 ≤ x < 0. Find the values of f(−1), f(−2), f(0), if they exist.
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`
Find x, if g(x) = 0 where g(x) = x3 − 2x2 − 5x + 6
Express the area A of a square as a function of its side s
Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?
Express the following logarithmic equation in exponential form
log2 64 = 6
Express the following logarithmic equation in exponential form
ln e = 1
Prove that alogcb = blogca
If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)
Answer the following:
Identify the following relation is the function? 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)}
Answer the following:
Let f: R → R be a function defined by f(x) = 5x3 – 8 for all x ∈ R, show that f is one-one and onto. Hence find f –1
Answer the following:
A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5
Answer the following:
Solve for x, logx (8x – 3) – logx 4 = 2
Answer the following:
Find the range of the following function.
f(x) = [x] – x
A function f is defined by f(x) = 2x – 3 find x such that f(x) = x
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
If f(x) = 5x - 3, then f-1(x) is ______
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
The domain of the function f defined by f(x) = `sqrt(4 - x) + 1/sqrt(x^2 - 1)` is equal to ______.
lf f : [0, ∞) `rightarrow` [0, ∞) and f(x) = `x/(1 + x)`, then f is ______.
