Deloitte Logarithms Questions and Answers 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

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

Given Exp. = log75/16 - 2 log5/9 + log32/243
= 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

log X+log Y=log (XY)
log (a²/bc) + log (b²/ac) + log (c²/ab)
=log [(a².b².c²)/(bc.ac.ab)]
=log [(a².b².c²)/(a².b².c²)]
=log 1=0

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

10^0.3010 = 2

=>0.3010 = log 2

So, log 2⁹ = 9 * log 2 = 9 * 0.3010 = 2.709

log10(10)+log10(10^2)+log10(10^3)+log10(10^4)+log10(10^5)

=log10(10*100*1000*10000*100000)

=log10(10^15)

=15log10(10)

=15

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

If

log 125 / log 5 = x

then

x = 3log5 / log5

=3