Advertisements
Advertisements
प्रश्न
Express the following logarithmic equation in exponential form
log2 64 = 6
उत्तर
| Logarithmic form | Exponential form |
| log2 64 = 6 | 26 = 64 |
APPEARS IN
संबंधित प्रश्न
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(b) {x : f(x) = −2}
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:
(iii) f g
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) \[2f - \sqrt{5} g\]
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
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
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 \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
The domain of the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is
The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is
Check if the following relation is function:
Check if the following relation is function:
Which of the following relations are functions? If it is a function determine its domain and range:
{(1, 1), (3, 1), (5, 2)}
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 2), (2, −1), (3, 1), (4, 3)}
Check if the relation given by the equation represents y as function of x:
2x + 3y = 12
Check if the relation given by the equation represents y as function of x:
x2 − y = 25
If f(m) = m2 − 3m + 1, find f(0)
If f(m) = m2 − 3m + 1, find `f(1/2)`
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
Express the following exponential equation in logarithmic form
`9^(3/2)` = 27
Find the domain of f(x) = ln (x − 5)
Prove that alogcb = blogca
Solve for x.
log2 + log(x + 3) – log(3x – 5) = log3
If f(x) = 3x + 5, g(x) = 6x − 1, then find (f − g) (2)
If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)
Answer the following:
Find whether the following function is one-one
f : R − {3} → R defined by f(x) = `(5x + 7)/(x - 3)` for x ∈ R − {3}
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Answer the following:
Find the range of the following function.
f(x) = [x] – x
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
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 real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
Find the range of the following functions given by `sqrt(16 - x^2)`
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.
