Quiz 1

log_x (0.1) = -1/3

=>log_x (1) - log_x (10) = -1/3

=>0 - log_x (10) = -1/3

=>log_x (10) = 1/3

=> 10 = x^(1/3)

=>x = 10³

=>x=1000

a^x = b^y

=> log a^x =log b^y

=>x(log a) = y(log b)

=>x/y = (log b)/(log a)

Let log be log to base 8
log [ x/6 ] = 1/3
x/6 = 8^(1/3)
x/6 = 2
x = 12

xy = x + y

xy - y = x

y (x - 1) = x

y = x / (x - 1)

log10(1/70)=log10 1- log 10 70
= 0-log10 (10*7)
=-((log10 10 )+(log10 7))
=- (1+a)

Log[(a+b)/3] = 0.5[log(a) + log(b)]
log[(a+b)/3] = 0.5*log(ab)
log[(a+b)/3] = log[sqrt(ab)]
(a+b)/3 = sqrt(ab)
a + b = 3*sqrt(ab)
a^{2} + 2ab + b^{2} = 9 ab
a^{2} + b^{2} = 7ab

Logx= log 3 + 2 log 2- (3/4) log 16.

= log3+log4- log 16^3/4

=log3+log4-log2^12/4

=log3+log4-log2³

=log(3*4/8)

=log(3/2)

Logx=log3/2

x=3/2

log₁₀₀₀₀ x = -1/4

=>x = 10000^(-1/4)

=>x = 1/10

3 - (1/2) log₃9

=3 - (1/2) log₃3²

=3 - (2/2)log₃3

=3 - 1

=2

log_e xy - log_e |x|

=log_e xy - log_e x  [As, inside log, variable can't be a nagetive one]

=log_e (xy/x)

=log_e y