मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Write the following expression as sum or difference of logarithm log(pqrs) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the following expression as sum or difference of logarithm

`log ("pq"/"rs")`

बेरीज

उत्तर

`log ("pq"/"rs")` = log (pq) – log (rs)  ...`[log  "m"/"n" = log"m" - log"n"]`

= log p + log q – (log r + log s)  ...[log mn = log m  log n]

= log p + log q – log r – log s

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Exercise 6.1 [पृष्ठ ११९]

APPEARS IN

संबंधित प्रश्‍न

Let A = {9, 10, 11, 12, 13} and let f: A → N be defined by f(n) = the highest prime factor of n. Find the range of f.


Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(c) whether f(xy) = f(x) : f(y) holds

 

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.

(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)} 


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: 

(iv) \[\frac{f}{g}\]

 

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)  \[2f - \sqrt{5} g\]

 

If f(x) = loge (1 − x) and g(x) = [x], then determine function:

(ii) fg


If fg and h are real functions defined by 

\[f\left( x \right) = \sqrt{x + 1}, g\left( x \right) = \frac{1}{x}\] and h(x) = 2x2 − 3, find the values of (2f + g − h) (1) and (2f + g − h) (0).
 
 

Write the range of the real function f(x) = |x|.

 

Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .

 

If f(x) = cos (loge x), then \[f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right) - \frac{1}{2}\left\{ f\left( xy \right) + f\left( \frac{x}{y} \right) \right\}\] is equal to

 

The domain of the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is

  

Let  \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?

 


If  \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then 

 


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) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.


If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x


Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}


If f(m) = m2 − 3m + 1, find f(0)


Express the area A of circle as a function of its circumference C.


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x3 


Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2


If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b


If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1


If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)


Answer the following:

Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not


Answer the following:

Simplify, log (log x4) – log (log x)


Answer the following:

Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3


Answer the following:

Solve : `sqrt(log_2 x^4) + 4log_4 sqrt(2/x)` = 2


Answer the following:

Find the domain of the following function.

f(x) = 5–xPx–1


A graph representing the function f(x) is given in it is clear that f(9) = 2

 Describe the following Domain


A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0


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


Find the domain of the following functions given by f(x) = `1/sqrt(x + |x|)`


Find the range of the following functions given by f(x) = |x − 3|


Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f + g)(x)


If f(x) = `log_e{((1 - x))/((1 - x))}, |x| < 1, f{(2x)/((1 + x^2))}` is equal to ______.


The ratio `(2^(log_2  1/4 a) - 3^(log_27(a^2 + 1)^3) - 2a)/(7^(4log_49a) - a - 1)` simplifies to ______.


If f : R – {2} `rightarrow` R i s a function defined by f(x) = `(x^2 - 4)/(x - 2)`, then its range is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×