CPhill

13^y  = 21     take the log of both sides

log 13^y = log 21   and we can write

y * log 13   = log 21    divide both sides by log 13

y  = log 21 / log 13  ≈ 1.187

Here yo go.....

(12)

10 + 5e^(2x) = 17     subtract 10 from both sides

5e^(2x)  = 7       divide by 5 on each side

e^(2x)  = 7/5  = 1.4      take the ln of both sides

lne^(2x)  = ln1.4      and we can write

(2x) * lne = ln 1.4     and ln e  = 1, so we can ignore this

2x = ln 1.4       divide by 2

x = [ln 1.4 ] / 2  ≈ .168

(11)

4e^x - 4 = 2     divide through by 2

2e^x - 2  = 1    add 2 to both sides

2e^x  =  3        divide both sides by 2

e^x = 3/2  = 1.5    take the ln of both sides

ln e^x = ln 1.5    and we can write

x * ln e = ln 1.5    and ln e  = 1, so we can ignore this

x = ln 1.5 ≈ .4055

We only need to show that two sides are parallel

The slope between  (0,5) and (6, -1)   =  [-1 - 5] / [6 - 0] =  -6/6 = -1

And the slope between (8,3) and (4,7) =  [7 - 3] / [ 4 - 8] = 4/-4 = -1

So  AB ll CD

Also  the distance between AD and BC are equal, so this is an isoceles trapezoid.

Here's  a pic......

6⁷ / 6⁵  =  6² =   36

4x-10+2x=4-2/3(6x-9)

4x -10  + 2x = 4 - 4x + 6    simplify

6x - 10  = 10 - 4x      add 10 to both sides

6x = 20 - 4x     add 4x to both sides

10x = 20     divide by 10 on both sides

x = 2

Well....swimming in salt water is easier {it's more buoyant}....just watch out for the jellyfish  ....!!!!

I'll toss you a lifesaver ring if you get near Shreveport.....LOL!!!!

LOL!!!......if the Atlantic HAS flooded......all that swimming practice is gonna' come in handy  !!!!!!