Advertisements
Advertisements
प्रश्न
Express the following exponential equation in logarithmic form
10−2 = 0.01
उत्तर
Exponential form | Logarithmic form |
10−2 = 0.01 |
– 2 = log10 (0.01) |
APPEARS IN
संबंधित प्रश्न
Define a function as a correspondence between two sets.
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
If \[f\left( x \right) = \frac{2x}{1 + x^2}\] , show that f(tan θ) = sin 2θ.
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are
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,
If \[3f\left( x \right) + 5f\left( \frac{1}{x} \right) = \frac{1}{x} - 3\] for all non-zero x, then f(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:
If f(m) = m2 − 3m + 1, find f(−3)
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
Check if the relation given by the equation represents y as function of x:
x + y2 = 9
Check if the relation given by the equation represents y as function of x:
x2 − y = 25
Find x, if g(x) = 0 where g(x) = 6x2 + x − 2
If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
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 ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
Simplify, log (log x4) – log (log x)
Answer the following:
If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k
Find the domain of the following function.
f(x) = `sqrtlog(x^2 - 6x + 6)`
An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x
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`
Calculate the value of `"gg" (1/2)`
If the domain of function f(a) = a2 - 4a + 8 is (-∞, ∞), then the range of function is ______
If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.