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

Select the correct answer from given alternatives. If log (5x – 9) – log (x + 3) = log 2 then x = ............... - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct answer from given alternatives.

If log (5x – 9) – log (x + 3) = log 2 then x = ...............

पर्याय

  • 3

  • 5

  • 2

  • 7

MCQ

उत्तर

If log (5x – 9) – log (x + 3) = log 2 then x = 5

Explanation:

log (5x – 9) – log (x + 3) = log 2

`therefore (5x - 9)/(x + 3) = 2`

`therefore 3x = 9 + 6`

∴ x = 5

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Miscellaneous Exercise 6.1 [पृष्ठ १२९]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 6 Functions
Miscellaneous Exercise 6.1 | Q I. (1) | पृष्ठ १२९

संबंधित प्रश्‍न

Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?


If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].

 

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 domain and range of function f(x) given by

\[f\left( x \right) = \frac{1}{\sqrt{x - \left| x \right|}}\] .
 

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

 

If f(x) = cos (log x), then the value of f(x2f(y2) −

\[\frac{1}{2}\left\{ f\left( \frac{x^2}{y^2} \right) + f\left( x^2 y^2 \right) \right\}\] is
 

The range of f(x) = cos [x], for π/2 < x < π/2 is


If A = {1, 2, 3} and B = {xy}, then the number of functions that can be defined from A into B is


If f(x) = sin [π2x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then


The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is

 

The range of  \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is 

 


If f(m) = m2 − 3m + 1, find f(−3)


Which of the following relations are functions? If it is a function determine its domain and range:

{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}


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


If f(x) = `{(x^2 + 3","  x ≤ 2),(5x + 7","  x > 2):},` then find f(2)


Check if the relation given by the equation represents y as function of x:

2y + 10 = 0


Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x


Find the domain and range of the follwoing function.

h(x) = `sqrt(x + 5)/(5 + x)`


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x2 


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x3 


Express the following exponential equation in logarithmic form

231 = 23


Express the following logarithmic equation in exponential form

log10 (0.001) = −3


Write the following expression as a single logarithm.

`1/3 log (x - 1) + 1/2 log (x)`


Answer the following:

Identify the following relation is the function? If it is a function determine its domain and range

{(12, 1), (3, 1), (5, 2)}


Answer the following:

Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`


Answer the following:

If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1


Given the function f: x → x2 – 5x + 6, evaluate f(x – 1)


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

Find the following values of the function 

(a) f(0)

(b) f(7)

(c) f(2)

(d) f(10)


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

For what value of x is f(x) = 1?


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

Find a and b


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`

Write an expression for gf(x) in its simplest form


Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x3 then, find the range of f


If a function f(x) is given as f(x) = x2 – 6x + 4 for all x ∈ R, then f(–3) = ______.


If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.


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)


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


Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x, and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×