English

Express the following logarithmic equation in exponential form In 12 = – 0.693 - Mathematics and Statistics

Advertisements
Advertisements

Question

Express the following logarithmic equation in exponential form

In `1/2` = – 0.693

Chart

Solution

Logarithmic form Exponential form
In `1/2` = – 0.693 `"e"^(-0.693) = 1/2`
shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Functions - Exercise 6.1 [Page 119]

RELATED QUESTIONS

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 X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.

(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

 

 


If  \[f\left( x \right) = \frac{1}{1 - x}\] , show that f[f[f(x)]] = x.

 

 


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

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

 

If f(x) = cos [π2]x + cos [−π2x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).


Let f and g be two functions given by

f = {(2, 4), (5, 6), (8, −1), (10, −3)} and g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, −5)}.

Find the domain of f + g


Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B? 

 


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


The range of the function  \[f\left( x \right) = \frac{x^2 - x}{x^2 + 2x}\]  is 

 

If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is

 

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


If  \[f\left( x \right) = 64 x^3 + \frac{1}{x^3}\] and α, β are the roots of \[4x + \frac{1}{x} = 3\] . Then,

 

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 

 


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

 


If f(m) = m2 − 3m + 1, find `f(1/2)`


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

{(0, 0), (1, 1), (1, −1), (4, 2), (4, −2), (9, 3), (9, −3), (16, 4), (16, −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, 0), (3, 3), (2, −1), (4, 1), (2, 2)}


Find x, if f(x) = g(x) where f(x) = x4 + 2x2, g(x) = 11x2


Express the following exponential equation in logarithmic form

3–4 = `1/81`


Write the following expression as a single logarithm.

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


Solve for x.

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


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:

Simplify `log_10  28/45 - log_10  35/324 + log_10  325/432 - log_10  13/15`


Find the domain of the following function.

f(x) = `sqrtlog(x^2 - 6x + 6)`


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

 Describe the following Domain


A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour


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)


Find the range of the following functions given by `|x - 4|/(x - 4)`


Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`


Find the domain of the following function given by:

f(x) = `(3x)/(2x - 8)`


Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3


If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.


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


The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×