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

Express the following exponential equation in logarithmic form 54° = 1 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Express the following exponential equation in logarithmic form

54° = 1

बेरीज

उत्तर

Exponential form Logarithmic form
54° = 1 0 = log54 1
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Functions - Exercise 6.1 [पृष्ठ ११९]

APPEARS IN

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.

 

A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [yf(y) = −1].


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

(iii) h(x) = x2 + 1

Find the range of function.


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(x) = (x − a)2 (x − b)2, find f(a + b).

 

If  \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).

 

 


Write the range of the function f(x) = ex[x]x ∈ R.

 

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


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  \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =

 

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,

 

The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is

 

Check if the following relation is a function.


Find the domain and range of the following function.

f(x) = `sqrt((x - 3)/(7 - x))`


Find the domain and range of the following function.

f(x) = `sqrt(16 - x^2)`


Express the following exponential equation in logarithmic form

25 = 32


Express the following exponential equation in logarithmic form

3–4 = `1/81`


Express the following exponential equation in logarithmic form

10−2 = 0.01


Express the following logarithmic equation in exponential form

log10 (0.001) = −3


Express the following logarithmic equation in exponential form

In `1/2` = – 0.693


Find the domain of f(x) = ln (x − 5)


Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b


If f(x) = 3x + 5, g(x) = 6x − 1, then find `("f"/"g") (x)` and its domain


Select the correct answer from given alternatives.

If log10(log10(log10x)) = 0 then x =


Answer the following:

Find whether the following function is one-one

f : R → R defined by f(x) = x2 + 5


Answer the following:

If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`


Find the domain of the following function.

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


Answer the following:

Find the range of the following function.

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


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)


Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`


A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`


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 the length of forehand of a person if the height is 53.3 inches


Find the domain of the following function.

f(x) = [x] + x


Find the range of the following functions given by `sqrt(16 - x^2)`


Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to ______.


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


Find the domain and range of the function f(x) = `1/sqrt(x - 5)`


If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×