CPhill

We have that

1  =  log_a 6

In exponential form, we  have

a^1  = 6

So..it's obvious that  a  = 6

Real part  :   -11

Imaginary part : 3i

Volume  =  (25 - 2x) (20 - 2x) x

f/r^2 + a  = n + k        subtract "a" from both sides

f/r^2 =  n + k  - a         multiply both sides  by r^2

f  = r^2 ( n + k  -a )     divide  both sides by (n + k  -a)

f / ( n + k - a)  = r^2       take  both roots

±√ [ f / ( n + k -a) ]  =  r   ⇒  first  answer

Power Property of Logarithms

Quotient Property of Logarithms

Equality Property of Logarithms

I'm not sure what "others"  you mean, Angel....

log ₅ x + log ₅ (x -5)  = 5

log ₅ [ x * (x - 5) ]  = 5        we have that

5^5   =  x ( x - 5)

5^5  = x^2 - 5x      rearrange as

x^2  - 5x - 5^5  = 0     solving this we have that

x  = [5 + 5√501] / 2    or  x  =  [ 5 - 5√501] / 2

The second answer results in the log of a negative

So....the only answer  is     x  =  [  5 + 5√501] / 2

  [ (x^2 + 2x -3)  / (x - 4)  ]  

_____________________

 [ (2x^2 + 5x - 3)  / ( x^2 - 16) ]

[ (x + 3) (x - 1) / (x -4) ]

___________________

 [ (2x - 1) ( x + 3) ] /  [ (x - 4) (x + 4) ]

[ ( x + 3) ( x - 1) / (x - 4)   *  [ (x - 4) ( x + 4) ] / [ (2x -1) ( x + 3) ]

[ ( x + 3) ( x - 1) ( x - 4) ( x + 4) ]

__________________________  

[ ( x -4) (2x - 1) ( x + 3) ]

[ (x -1) ( x + 4) ]

____________

    2x  - 1

x^2  + 3x  - 4

___________

  2x  - 1

V_cyinder  =  pi ( r)^2 * h

182 = pi ( r)^2 * (1/2)r      multiply both sides  by 2

364  = pi * r^3     divide  both sides by pi

364 / pi  = r^3   take the cube root of both sides

∛ [ 364 / pi ]  = r

The surface area is  given by :

( 2pi * r * h )  + ( 2 * pi * r^2)  =   2pi [ 2* r * h + r^2 ]  =  2pi  [ 2r * (1/2)r + r^2 ]  = 2 pi (2)r^2 = 4pi r^2

So.....subbing for  r, we have

4 pi [ ∛ [ 364 / pi ] ]^2  ≈ 298.66 units^2

arccos  [ -√2 / 2 ] =       3pi/ 4  rads