Question

If log x = 1/2 log a - log b and a = 4b^2, then x =
(a) 1
(b) 2
(c) 4
(d) 8
(e) 16

Answer 1

ok let a=4b^2 in the above
log x=1/2log (4b^2)-log b
or using property of log
\[\Large \log x=\log (4b^2)^{\frac{1}{2}}-\log b\]
\[\Large \log x=\log(2b)-\log(b)\]
now again using log property
\[\Large \log x=\log(2b/b)\]
\[\Large \log x= \log 2\]

Answer 2

@waterineyes do not you think it should be x=2 ??

Answer 3

\[\log(x) = \frac{1}{2}\log(2b)^2 - \log(b) \implies \log(x) = \frac{1}{2} \times 2 \log(2b) - \log(b)\]

\[\log(x) = \log(2b) - \log(b) = \implies \log(x) = \log(2) \implies \color{blue}{ x = 2}\]

Answer 4

Yeah sorry my mistake there @sami-21

Answer 5

its ok :)
i do a lot of mistakes .
i am notorious for typo mistakes here :P
ask anyone here :P

Answer 6

@lawls understood or any problem anywhere ??

Answer 7

hold on i'm reading what u guys wrote

Answer 8

Take your time..

Answer 9

ok i'm done reading. thanks alot guys i fully understand now :)

Answer 10

Sure ??

Answer 11

yeah x is 2 right?

Answer 12

yes x=2