हिंदी

Express the following exponential equation in logarithmic form 3–4 = 181 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Express the following exponential equation in logarithmic form

3–4 = `1/81`

योग

उत्तर

3–4 = `1/81`

∴ – 4 = `log_3 (1/81)`   …[By definition of logarithm]

i.e. `log_3 (1/81)` = – 4

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Functions - Exercise 6.1 [पृष्ठ ११९]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 6 Functions
Exercise 6.1 | Q 17. (e) | पृष्ठ ११९

संबंधित प्रश्न

Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:

(b) pre-images of 6, −3 and 5.

 

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 A = [pqrs] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?


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: 

(i) 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: 

(vii) f2 + 7f


Write the domain and range of the function  \[f\left( x \right) = \frac{x - 2}{2 - x}\] .

 

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

 

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(x) = x, \[g\left( x \right) = \frac{1}{x}\]  and h(x) = f(xg(x). Then, h(x) = 1


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 definition of  \[f\left( x \right) = \sqrt{4x - x^2}\] is 

 

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

 

The range of the function f(x) = |x − 1| is


Check if the following relation is function:


Check if the following relation is function:


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 : N → N given by f(x) = x2 


Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2


Express the following logarithmic equation in exponential form

log10 (0.001) = −3


Express the following logarithmic equation in exponential form

ln e = 1


Find the domain of f(x) = ln (x − 5)


Write the following expression as sum or difference of logarithm

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


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:

A function f : R → R defined by f(x) = `(3x)/5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f–1


Answer the following:

A function f is defined as f(x) = 4x + 5, for – 4 ≤ x < 0. Find the values of f(–1), f(–2), f(0), if they exist


Answer the following:

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5


Answer the following:

For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3


Answer the following:

If `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b


Answer the following:

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


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - x^2) + sqrt(5 - x)`


Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?


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

Describe the following Range


A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2


The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______


If f(x) = 5x - 3, then f-1(x) is ______ 


If f(x) = `1/sqrt(4 - 3x)`, then dom(f) = ______..


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


Find the domain of the following functions given by f(x) = x|x|


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×