Advertisements
Advertisements
Question
Find the value of the product: `|(log_3 64, log_4 3),(log_3 8, log_4 9)| xx |(log_2 3, log_8 3),(log_3 4, log_3 4)|`
Advertisements
Solution
`|(log_3 64, log_4 3),(log_3 8, log_4 9)| xx |(log_2 3, log_8 3),(log_3 4, log_3 4)| = |(log_3 64 * log_2 3 + log_4 3 * log_3 4, log_3 64 * log_8 3 + log_4 3 * log_3 4),(log_3 8 * log_2 3 + log_4 9 * log_3 4, log_2 8 * log_8 3 +log_4 9 * log_3 4)|`
= `|(log_2 64 + log_3 3, log_8 64 + log_3 3),(log_2 8 +log_3 9, log_8 8 + log_3 9)|`
`log_"b" "a" * log_"c" "b" = log_"c" "a"`
⇒ `log_"a" "a"` = 1
= `|(log_2 2^6 + 1, log_8 8^2 + 1),(log_2 2^3 + log_3 3^2, 1 + log_3 3^2)|`
= `|(6log_2 2 + 1, 2log_8 8 + 1),(3log_2 2 + 2log_3 3, 1 + 2log_3 3)|`
= `|(6 + 1, 2 + 1),(3 + 2, 1 + 2)|`
= `|(7, 3),(5, 3)|`
= 21 – 15
= 6
APPEARS IN
RELATED QUESTIONS
Without expanding the determinant, prove that `|("s", "a"^2, "b"^2 + "c"^2),("s", "b"^2, "c"^2 + "a"^2),("s", "c"^2, "a"^2 + "b"^2)|` = 0
Prove that `|(1 + "a", 1, 1),(1, 1 + "b", 1),(1, 1, 1 + "c")| = "abc"(1 + 1/"a" + 1/"b" + 1/"c")`
Prove that `|(1, "a", "a"^2 - "bc"),(1, "b", "b"^2 - "ca"),(1, "c", "c"^2 - "ab")|` = 0
Show that `|("a"^2 + x^2, "ab", "ac"),("ab", "b"^2 + x^2, "bc"),("ac", "bc", "c"^2 + x^2)|` is divisiible by x4
If a, b, c, are all positive, and are pth, qth and rth terms of a G.P., show that `|(log"a", "p", 1),(log"b", "q", 1),(log"c", "r", 1)|` = 0
Without expanding, evaluate the following determinants:
`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`
If A is a Square, matrix, and |A| = 2, find the value of |A AT|
Determine the roots of the equation `|(1,4, 20),(1, -2, 5),(1, 2x, 5x^2)|` = 0
Solve the following problems by using Factor Theorem:
Show that `|(x, "a", "a"),("a", x, "a"),("a", "a", x)|` = (x – a)2 (x + 2a)
Solve that `|(x + "a", "b", "c"),("a", x + "b", "c"),("a", "b", x + "c")|` = 0
Show that `|("b" + "C", "a", "a"^2),("c" + "a", "b", "b"^2),("a" + "b", "c", "c"^2)|` = (a + b + c)(a – b)(b – c)(c – a)
If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k
Identify the singular and non-singular matrices:
`[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`
Identify the singular and non-singular matrices:
`[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`
Choose the correct alternative:
If A = `[("a", x),(y, "a")]` and if xy = 1, then det(AAT) is equal to
If P1, P2, P3 are respectively the perpendiculars from the vertices of a triangle to the opposite sides, then `cosA/P_1 + cosB/P_2 + cosC/P_3` is equal to
If f(x) = `|(cos^2x, cosx.sinx, -sinx),(cosx sinx, sin^2x, cosx),(sinx, -cosx, 0)|`, then for all x
Let a, b, c, d be in arithmetic progression with common difference λ. If `|(x + a - c, x + b, x + a),(x - 1, x + c, x + b),(x - b + d, x + d, x + c)|` = 2, then value of λ2 is equal to ______.
Let S = `{((a_11, a_12),(a_21, a_22)): a_(ij) ∈ {0, 1, 2}, a_11 = a_22}`
Then the number of non-singular matrices in the set S is ______.
