Mahindra Comviva Logarithms Problems with Solutions Quiz -1

log ₂ x = 10 ⇒ x = 2¹⁰.
∴ log _x y = 100
⇒ y = x¹⁰⁰
⇒ y = (2¹⁰)¹⁰⁰ [put value of x]
⇒ y = 2¹⁰⁰⁰.

log(ab²) - log(ac) + log(abc⁴) - 3log(bc)
= log(ab²) - log(ac) + log(abc⁴) - log(b³c³)
= log_a(ab²/ac)*(abc⁴/b³c³)
= log_aa = 1

a log10 m = blog1000 m log10 ma = log1000 mb
log10 ma = log103 mb log10 ma = log10(mb)1/3

log10 ma = log10 mb/3 ma = mb/3

a =
b
3


b = 3a

1
logxyxyz
+
1
logyzxyz
+
1
logzxxyz
= logxyz xy + logxyz yz + logxyz zx
= logxyz(xy x yz x zx)

= logxyz(xyz)2

= 2logxyzxyz
= 2 x 1 = 2

Let log327 = x
3x = 27

3x = 33

x = 3

log(K2 - 4K + 5) = 0
log(K2 - 4K + 5) = log1 ( log 1 = 0)


K2 - 4K + 5 = 1

K2 - 4K + 4 = 0

(K - 2)2 = 0 K = 2

Characteristic = 3 -1 = 2

Log4 log2 log3 (2x - 1) =
1
2


log2 log3 (2x - 1) = 41/2 = 2


log3 (2x - 1) = 22 = 4

2x - 1 = 34 = 81
2x = 82
x = 41

logab =
log b
log a
, logbc =
log c
log b
, logca =
log a
log c


logab x logbc x logca =
log b
log a
x
log c
log b
x
log a
log c
=
1
2
x
1
3
x
k
5



1 =
k
30



k = 30

Given Exp. = log75/16 – 2 log5/9 + log32/343 = log [(25 x 3) / (4 x 4)] – log (25/81) + log [(16 x 2) / (81 x 3)] = log(25 x 3) – log ( 4 x 4 ) – log(25) + log81 + log(16 x 2) -log (81 x 3) = log 25 + log 3 – log 16 – log 25 + log 81 + log 16 + log 2 – log 81 – log 3 = log 2