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If a,b,c are distinct real number differ...

If a,b,c are distinct real number different from 1 such that
`(log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0`, then abc is equal to

A

0

B

e

C

1

D

none of these

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AI Generated Solution

To solve the given equation: \[ (\log_b a \cdot \log_c a - \log_a a) + (\log_a b \cdot \log_c b - \log_b b) + (\log_a c \cdot \log_b c - \log_c c) = 0 \] we will follow these steps: ...
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ALLEN-BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -ILLUSTRATIONS
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  2. If log(a)x = p and log(b)x^(2) =q, then log(x)sqrt(ab) is equal to (wh...

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  3. If a,b,c are distinct real number different from 1 such that (log(b)...

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  4. Evaluate: 81^(1//log(5)3) + 27^(log(9)36) + 3^(4//log(l)9)

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  5. Solve for x: a) log(0.5)(x^(2)-5x+6) ge -1, b) log(1//3)(log(4)(x^(2)-...

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  6. Solve the following - (a)" " log(2)xle(2)/(log(2)x-1)" "

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  7. Solve the equation: log(2x+3)x^(2) lt log(2x)(2x+3)

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  8. Solve for x:2^(x+2) gt (1/4)^(1/x)

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  9. Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))

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  10. Show that log(4)18 is an irrational number.

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  11. If in a right angled triangle, a and b are the lengths of sides and c ...

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  12. If the arcs of same length in two circles subtend angles of 60^(@) and...

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  13. If sintheta+sin^(2)theta=1, then prove that cos^(12)theta+3cos^(10)the...

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  14. 4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)is equal to

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  15. If sintheta=-1/2 and tantheta=1/sqrt(3) then theta is equal to,

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  16. Prove that sqrt(3) " cosec "20^(@)-sec 20^(@)=4

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  17. Prove that tan 70^(@)=cot70^(@)+2cot40^(@)

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  18. If sin 2A=lambda sin 2B, prove that : (tan (A+B))/(tan(A-B)) = (lambda...

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  19. (sin5theta+sin2theta-sin tehta)/(cos5theta+2cos3theta+2cos^(2)theta+co...

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  20. Prove that: s in 12^0s in 48^0s in 54^0=1/8dot

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