SapientRazorFish Problems on Logarithms with answers

Question #1

log xY = 100 and log x2 = 10, then the value of y is
Question Explanation

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

Question #2

What is the value of log(ab^2) - log(ac) + log(abc^4) - 3log(bc)?
Question Explanation

log(ab2) - log(ac) + log abc4 - 3log(bc)
= log ab2 - logac + log abc4 - log b3c3

= loga
ab2
ac
x
abc4
b3c3


loga a = 1

Question #3

The value of log 9/8 - log 27/32 + log3/4 is ?
Question Explanation

Given Exp. = log [{(9/8) / (27/32)} x 3/4)]
= log [(9/8) x (3/4) x (32/27)]
= log 1
= 0

Question #4

The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?
Question Explanation

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

Question #5

Find the value of log (a^2 / bc) + log (b^2 / ac) + log (c^2 / ab) ?
Question Explanation

logX+logY=log(XY)
log(a2/bc)+log(b2/ac)+log(c2/ab)
=log(a2 b2 c2 b/cacab)
=log(a2 b2c2/ a2b2c2)
=log1=0

Question #6

The equation loga (x) + loga (1+x)=0 can be written as ?
Question Explanation

loga(x) +loga(1+x) = 0


we know that log a1 =0

=>log a (x) + log (1+x) =0
=>log a (x) + log (1+x) = log a 1

Question #7

If 10^0.3010 = 2, then find the value of log0.125 (125) ?
Question Explanation

log0.5 = -0.3010
log0.5 = -0.3010
1 -.301 = .699

Question #8

log10 (10) + log10 (100) + log10 (1000) + log10 (10000) + log10 (100000)
is equal to ?
Question Explanation

1 + 2 + 3 + 4 + 5
= 15

Question #9

The value of log2 (1/64) is?
Question Explanation

log2(164)=xlog2(164)=x
Rewrite the equation as x=log2(164)x=log2(164).
x=log2(164)x=log2(164)
Logarithm base 22 of 164164 is −6-6.
x=−6

Question #10

If log 125 / log 5 = x, then x is equal to ?
Question Explanation

If log 125 / log 5 = x
then x = 3log5 / log5= 3

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