Advertisements
Advertisements
प्रश्न
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
उत्तर
Let `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)` = k
∴ log a = k(x + y – 2z), log b = k(y + z – 2x), log c = k(z + x – 2y)
∴ log a + log b + log c = k(x + y – 2z) + k(y + z – 2x) + k(z + x – 2y)
∴ log abc = k(x + y – 2z + y + z – 2x + z + x – 2y) = 0
∴ log abc = log 1 ...[∵ log 1 = 0]
∴ abc = 1
APPEARS IN
संबंधित प्रश्न
Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.
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.
(a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}
Let A = [p, q, r, s] and B = [1, 2, 3]. Which of the following relations from A to B is not a function?
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
Write the domain and range of function f(x) given by
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
If \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + y) f(x − y) is equal to
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 \[f\left( x \right) = \sqrt{x - 3 - 2\sqrt{x - 4}} - \sqrt{x - 3 + 2\sqrt{x - 4}}\] is
The range of the function f(x) = |x − 1| is
If f(m) = m2 − 3m + 1, find f(−3)
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 2), (2, −1), (3, 1), (4, 3)}
Find x, if g(x) = 0 where g(x) = 6x2 + x − 2
Find the domain and range of the following function.
f(x) = `root(3)(x + 1)`
Check the injectivity and surjectivity of the following function.
f : R → R given by f(x) = x2
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x3
Express the following logarithmic equation in exponential form
log2 64 = 6
Write the following expression as a single logarithm.
5 log x + 7 log y − log z
Solve for x.
log2 + log(x + 3) – log(3x – 5) = log3
If `log((x + y)/3) = 1/2 log x + 1/2 logy`, show that `x/y + y/x` = 7
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Select the correct answer from given alternative.
The domain and range of f(x) = 2 − |x − 5| is
Answer the following:
Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Show that, logy x3 . logz y4 . logx z5 = 60
Answer the following:
If a2 = b3 = c4 = d5, show that loga bcd = `47/30`
Answer the following:
Find the domain of the following function.
f(x) = x!
Answer the following:
Find the range of the following function.
f(x) = [x] – x
Answer the following:
Find (f ° g) (x) and (g ° f) (x)
f(x) = `x/(x + 1)`, g(x) = `x/(1 - x)`
Given the function f: x → x2 – 5x + 6, evaluate f(2a)
Given the function f: x → x2 – 5x + 6, evaluate f(2)
The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`
Calculate the value of `"gg" (1/2)`
Domain of function f(x) = cos–1 6x is ______.
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 ______
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Find the range of the following functions given by f(x) = 1 – |x – 2|
The value of the function f(x) = `(x^2 - 3x + 2)/(x^2 + x - 6)` lies in the interval
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.
