Advertisements
Advertisements
प्रश्न
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
विकल्प
3
5
2
7
उत्तर
If log (5x – 9) – log (x + 3) = log 2 then x = 5
Explanation:
log (5x – 9) – log (x + 3) = log 2
`therefore (5x - 9)/(x + 3) = 2`
`therefore 3x = 9 + 6`
∴ x = 5
APPEARS IN
संबंधित प्रश्न
Let f : R → R and g : C → C be two functions defined as f(x) = x2 and g(x) = x2. Are they equal functions?
f, g, h are three function defined from R to R as follow:
(ii) g(x) = sin x
Find the range of function.
et A = (12, 13, 14, 15, 16, 17) and f : A → Z be a function given by
f(x) = highest prime factor of x.
Find range of f.
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:
(i) f + g
Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (f + g) (x), (f − g) (x), (fg) (x) and \[\left( \frac{f}{g} \right) \left( x \right)\] .
Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .
Let A and B be two sets such that n(A) = p and n(B) = q, write the number of functions from A to B.
If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is
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,
If f : R → R be given by for all \[f\left( x \right) = \frac{4^x}{4^x + 2}\] x ∈ R, then
The domain of the function
Check if the following relation is function:
If f(m) = m2 − 3m + 1, find f(0)
If f(m) = m2 − 3m + 1, find f(− x)
Check if the relation given by the equation represents y as function of x:
2y + 10 = 0
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((x - 2)(5 - x)`
Express the area A of a square as a function of its perimeter P
Express the following exponential equation in logarithmic form
25 = 32
Express the following exponential equation in logarithmic form
e2 = 7.3890
Express the following exponential equation in logarithmic form
`"e"^(1/2)` = 1.6487
Write the following expression as sum or difference of logarithm
`log ("pq"/"rs")`
If f(x) = ax2 − bx + 6 and f(2) = 3 and f(4) = 30, find a and b
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
Answer the following:
Let f : R – {2} → R be defined by f(x) = `(x^2 - 4)/(x - 2)` and g : R → R be defined by g(x) = x + 2. Examine whether f = g or not
Answer the following:
Simplify `log_10 28/45 - log_10 35/324 + log_10 325/432 - log_10 13/15`
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - 3) + 1/(log(5 - x))`
Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?
A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0
If f(x) = 5x - 3, then f-1(x) is ______
Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______
The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.
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 ______.
Let f and g be two functions given by f = {(2, 4), (5, 6), (8, – 1), (10, – 3)} g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, – 5)} then. Domain of f + g is ______.
Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (f – g)(x)
Let f(x) = `sqrt(1 + x^2)`, then ______.
If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.
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 ______.
If f: R `rightarrow` R be a function defined by f(x) = 4x3 – 7. Then ______.