AzizHusain

12) ln 9 + ln 2 --> ln(9*2) = ln(18).

16) ln(a) - 2 ln b + 1/3 ln c --> ln(a) - ln(b^2) + ln(c^1/3) --> ln (a/(b^2)*c^1(/3)).

24) ln(x-1) / 2 = 4 --> ln(x-1) = 8 --> e^(ln(x-1)) = e^8 --> x - 1 = e^8 --> x = e^8 + 1 = 2981.9579870417282747. 

32) e^(x) / 2 = 5 --> e^x = 10 --> ln(e^x) = ln(10) --> x = ln(10) = 2.3025850929940457.

 $$3^{2x} = 27

3^{2x} = 3^3

2x = 3

\mathbf{x = 3/2.}$$

$$3^{-2x+2} = 81

3^{-2x+2} = 3^4

-2x+2 = 4

-2x = 2

x = -1.$$

$$4^{x} = 19

log 4^{x} = log 19

x log 4 = log 19

x = log 19 \div\;log 4.

x = 2.1239637567217926.$$

3^x - 1 = 72

3^x = 73

log(3^x) = log 73

x log 3 = log 73

x = log 73 / log 3 

x = 3.9053444835847247.

$$log(2x) = -1

10^{log(2x)} = 10^-1

2x = 0.1

x = 0.1 \div \; 2

x = 0.05.$$

$$log(x) - log(3) = 8

log(x \div \; 3) = 8

10^{(log(x \div \; 3)} = 10^8

x \div \; 3 = 10^8

x = 3*10^8

x = 300000000.$$

On mine, the link is doing nothing but appearing like the normal google sign. :(

Oh, I see..well looks like lots of fun! 

Oh, neat!! What's the last picture...looks like a dragon!

Sounds very festive, rosala!  It must have been extremely fun!

Also, yes, the PM did a wonderful thing meeting children personally without interference...usually so much security would be there for presidents but it just shows how approachable and friendly he can be...

I see. Yes, must be lots on social media websites and other places. 

This is not that crucial of a matter, but: Is it just me or do we have to hit enter twice to create a single space...because when I am making a post, I have to create a double space, but it appears as a single space once I see the created post.

I see. Oh, yes, the number 68 this time and nice canon and close-up pics! The close-ups really do let you feel the emotions and wonder!

The children must be proud to do it for their country so that's good although the work may be tough. It reminds me of the opening ceremonies in the Olympics.

Ah, very beautiful...like art! The different colors really make a nice impression and the flag that is just made of bodies is incredible (pretty accurate, too!).

Oh, I see. Yes, practice makes perfect . Also, it must be great to come together as one and make the most out of the liberation day! I wonder how long it takes to choose all the right children, too!

Wow, amazing!! Love the colors and the mass participation!! I have never been near the Red Fort area, but anyway, the celebration this year must have been even merrier with the new prime minister!