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

Write the following expression as sum or difference of logarithm log(xy3) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the following expression as sum or difference of logarithm

`log (sqrt(x) root(3)(y))`

बेरीज

उत्तर

`log (sqrt(x) root(3)(y)) = log x^(1/2) + logy^(1/3)`

= `1/2logx + 1/3logy`

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

APPEARS IN

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?


fgh are three function defined from R to R as follow:

(iii) h(x) = x2 + 1

Find the range of function.


The function f is defined by \[f\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 3 \\ 3x, & 3 \leq x \leq 10\end{cases}\]

The relation g is defined by \[g\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 2 \\ 3x, & 2 \leq x \leq 10\end{cases}\]

Show that f is a function and g is not a function.


If  \[f\left( x \right) = \begin{cases}x^2 , & \text{ when }  x < 0 \\ x, & \text{ when }  0 \leq x < 1 \\ \frac{1}{x}, & \text{ when }  x \geq 1\end{cases}\]

find: (a) f(1/2), (b) f(−2), (c) f(1), (d)

\[f\left( \sqrt{3} \right)\] and (e) \[f\left( \sqrt{- 3} \right)\]
 

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: 

(vii) f2 + 7f


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

(ii) fg


Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.


Let f and g be two real functions given by

f = {(0, 1), (2, 0), (3, −4), (4, 2), (5, 1)} and g = {(1, 0), (2, 2), (3, −1), (4, 4), (5, 3)}

Find the domain of fg.


If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right)\] , then \[f\left( \frac{2x}{1 + x^2} \right)\]  is equal to

 

 


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

 

Check if the following relation is function:


If f(m) = m2 − 3m + 1, find f(0)


If f(m) = m2 − 3m + 1, find f(−3)


If f(x) = 3x + a and f(1) = 7 find a and f(4).


If f(x) = `{(x^2 + 3","  x ≤ 2),(5x + 7","  x > 2):},` then find f(0)


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

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


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:

x + y2 = 9


Find x, if g(x) = 0 where g(x) = 6x2 + x − 2


Express the following exponential equation in logarithmic form

`9^(3/2)` = 27


Prove that logbm a = `1/"m" log_"b""a"`


Solve for x.

2 log10 x = `1 + log_10 (x + 11/10)`


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


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:

If f(x) = 3x + a and f(1) = 7 find a and f(4)


Answer the following:

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


Answer the following:

Solve for x, logx (8x – 3) – logx 4 = 2


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`


Answer the following:

Find the range of the following function.

f(x) = `x/(9 + x^2)`


Answer the following:

Find (f ° g) (x) and (g ° f) (x)

f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`


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


The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.


Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______ 


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


Find the domain of the function f given by f(x) = `1/sqrt([x]^2 - [x] - 6)`


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 ______.


The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval


The range of the function y = `1/(2 - sin3x)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×