हिंदी

Express the following logarithmic equation in exponential form ln 1 = 0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Express the following logarithmic equation in exponential form

ln 1 = 0

सारिणी

उत्तर

Logarithmic form Exponential form
ln 1 = 0 e0 = 1
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 18. (e) | पृष्ठ ११९

संबंधित प्रश्न

Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(c) whether f(xy) = f(x) : f(y) holds

 

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) \[f\left( \sqrt{- 3} \right)\]
 

If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]

 

 


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

 

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

 


The domain of definition of  \[f\left( x \right) = \sqrt{\frac{x + 3}{\left( 2 - x \right) \left( x - 5 \right)}}\] is 

  

The domain of definition of the function f(x) = log |x| is


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

 

If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`


Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`


If f(x) = `("a" - x)/("b" - x)`, f(2) is undefined, and f(3) = 5, find a and b


Find the domain and range of the following function.

f(x) = `root(3)(x + 1)`


lf f(x) = 3(4x+1), find f(– 3)


Express the following exponential equation in logarithmic form

231 = 23


Express the following logarithmic equation in exponential form

log2 64 = 6


Express the following logarithmic equation in exponential form

ln e = 1


Find the domain of f(x) = log10 (x2 − 5x + 6)


Write the following expression as sum or difference of logarithm

In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`


Write the following expression as sum or difference of logarithm

In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`


Write the following expression as a single logarithm.

ln (x + 2) + ln (x − 2) − 3 ln (x + 5)


If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy 


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


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:

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


Answer the following:

Find x, if x = 33log32  


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 function f is defined by f(x) = 2x – 3 find x such that f(x) = 0


The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.


The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.


Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.


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


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


If f(x) = `(x - 1)/(x + 1)`, then show that `f(- 1/x) = (-1)/(f(x))`


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


The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.


Let f(θ) = sin θ (sin θ + sin 3θ) then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×