Today is our topic of discussion Exponential and Logarithmic Function exercises – 9.2 .
Exponential and Logarithmic Function exercises – 9.2
1. Which is the simplest form of the expression
1) 0
2) 1
3) a
4) x
2. If a, b, p>0 and a ≠1, b≠1 then
(i) log(aP)=log(bP)x log(ab)
(ii) logax√axlogb√bx x logc√c’s value is 2
(iii) xlogay=ylogaz
Which combination of these statements is correct?
1) i and ii
2) ii and iii
3) i and iii
4) i, ii and iii
Answer questions 3-5 when x, y, z ≠ 0 and a^x = b^x = c^x
3. Which is correct?
1) a = bxy/z
2) a = cxxy
3) a = căx
4. Which of the followings is equal to ac?
1) b(y/x) . b(y/z)
2) b(y/x) . b(x/y)
3) b(y/x) . b(x/y)
4) b(y/x) . b(x/y)
5. If b² ac, which one is correct?
1) 1/x+1/z=2/y
2) 1/y+1/z=2/z
3) 1/y+1/z=2/x
4) 1/x+1/y=2/z
6. Show that,
7.
5) If a³-x b5x = a(5+z)b(3+x) then show that, xlogk(b/a) =logka
6) If xy(a-1) = p, xy(b−1) = q, xy(c-1) = r then show that, (b-c)logkp+ (c-a)logkq + (a – b)log(kxr) = 0
8. Sketch the graph:
1) y = 3x
2) y = -3x
3) y = 3(x+1)
4) y = -3(x+1)
5) y = 3 (- x + 1)
6) y = 3 (x – 1)
9. Write down the inverse function in each case, mention the domain and range and sketch the graph:
1) y = 1 – 2^x
2) y = log_10(x)
3) y = x², x > 0
10. Determine f(x) = ln(x – 2) function’s domain D_{f} and range R_{f} . f(x) = ln((1 – x)/(1 + x))
11. Determine function’s domain and range.
12. Sketch the graph mentioning domain and range:
1) f(x) = |x| , when – 5 <= x <= 5
2) f(x) = x + |x| when – 2 <= x <= 2
13. Given, 2^(2x) . 2^(y – 1) = 64…….(i) and 6x . (6^(y – 2) / 3 =72…..(ii)
1) Convert (i) and (ii) into linear equation of x and y.
2) Solve the equations and verify them.
3) Should x and y be lengths of two adjacent sides of a quadrilateral and the angle included them be 90°, state whether the quadrilateral would be a rectangle or a square; find its area and the lengths of the diagonals.
14. Given, y = 2^x
1) Mention the domain and range of the function.
2) Draw the graph of the function, and mention its salient features.
3) State whether the given function has an inverse function. If so, is it one-one? Sketch the graph of the inverse function.
15. f(x)=3(2x+2) and g(x) = 27(x+1)
1) Find the domain of f(x).
2) If f(x)+g(x) = 36 then find the value of x.
3) If q(x) = gx/fx then, sketch the graph of q(x) and determine domain and range.
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