Advertisements
Advertisements
Question
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Options
4, −4
4
−4
not defined
Solution
4
Explanation:
2 log2 x = 4, x > 0
∴ log2 (x2) = 4
∴ x2 = 16
∴ x = ± 4
∴ x = 4
APPEARS IN
RELATED QUESTIONS
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:
(ii) g − f
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(i) f + g
Write the range of the real function f(x) = |x|.
Write the range of the function f(x) = sin [x], where \[\frac{- \pi}{4} \leq x \leq \frac{\pi}{4}\] .
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
If f(x) = cos (log x), then the value of f(x2) f(y2) −
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
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
If \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) =
The function f : R → R is defined by f(x) = cos2 x + sin4 x. Then, f(R) =
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
Check if the relation given by the equation represents y as function of x:
3x − 6 = 21
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find x, if g(x) = 0 where g(x) = 6x2 + x − 2
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Find the domain and range of the following function.
f(x) = `sqrt(16 - x^2)`
Express the following exponential equation in logarithmic form
231 = 23
Express the following exponential equation in logarithmic form
e–x = 6
Find the domain of f(x) = log10 (x2 − 5x + 6)
If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
Select the correct answer from given alternatives.
If log10(log10(log10x)) = 0 then x =
Select the correct answer from given alternatives.
If f : R → R is defined by f(x) = x3 then f–1 (8) is equal to :
Select the correct answer from given alternative.
The domain and range of f(x) = 2 − |x − 5| is
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:
For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3
Answer the following:
Find x, if x = 33log32
Answer the following:
Show that, `log ("a"^2/"bc") + log ("b"^2/"ca") + log ("c"^2/"ab")` = 0
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Find the domain of the following function.
f(x) = `sqrtlog(x^2 - 6x + 6)`
A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`
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
Let f : R → R be defined by
f(x) = `{(3x; x > 2),(2x^2; 1 ≤ x ≤ 2), (4x; x < 1):}`
Then f(-2) + f(1) + f(3) is ______
The domain and range of the real function f defined by f(x) = `(4 - x)/(x - 4)` is given by ______.
If f(x) = `log_e{((1 - x))/((1 - x))}, |x| < 1, f{(2x)/((1 + x^2))}` is equal to ______.
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
The domain of the function f(x) = `1/sqrt(|x| - x)` is ______.
The range of the function f(x) = x2 + 2x+ 2 is ______.
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.
The period of the function
f(x) = `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` is ______.