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Well I swear it's the only information I have. This is part of a work for my math class. This was verified by my professor and he says that it is possible to find an answer with these information.

... meh I'm quite puzzled to!

Can I have an in depth explanation for the following:

" Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
9/2 log(5) x = 4 log(5) (2 x-1)  "

Pi x Pi =Pi^2

You must know beforehand what the result is in order to solve for x. This expression:

log (  (1000(square root of ( (10^x)^3) ) ) /(10^x)^-1)=?. In other words:? must equal something!!.

Solve for x over the real numbers:
5^((9 x)/2) = 625^(2 x-1)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
9/2 log(5) x = 4 log(5) (2 x-1)

Expand out terms of the right hand side:
9/2 log(5) x = 8 log(5) x-4 log(5)

Subtract 8 x log(5) from both sides:
-7/2 log(5) x = -4 log(5)

Divide both sides by -(7 log(5))/2:
Answer: |x = 8/7

1/12

Hint:

Express the RHS as ( (4^x - 2) + (2^x - 4) )^3

Expand as:  (4^x - 2)^3 + (2^x - 4)^3 + 3(4^x - 2)^2(2^x - 4) + 3(4^x - 2)(2^x - 4)^2

Set this equal to the LHS and rearrange to get (4^x - 2)(2^x - 4)(4^x + 2^x - 6) = 0

I'll leave you to take it from here! 

.

if tan(x) = y, then tan^-1(y) = x

Will use the reciprocal of the numbers stated:

The difference between 13th term - 5th term=8

The difference between their values: 178 - 28 =150

Therefore, the common difference is:150/8 =18.75

a(5)=F + (5 - 1).18.75

28 =F + 75

F=28 - 75 =-47. Now, we use the reciprocal of the answer:

-1/47 - The first term. Similarly,................(1)

a(13)=F + (13 -1).18.75

178 =F + 225

F=178 - 225

F=-47 or -1/47 - The first term..................(2)

You mean: 9=1.1^y?  If so, take the log of both sides:

Log(9)=y x Log(1.1)

y=Log(9) / Log(1.1)

y=~23.05

Simply add the range to the smallest number.

(b).   x = 4,  y = 9,  z = 25

(by inspection)

.

(a).  (sqrt(x) + sqrt(y) + sqrt(z))^2 = x + y + z + 2(sqrt(xy) + sqrt(xz) + sqrt(yz))

LHS = 10^2 = 100.                          RHS = 38 + 2*30 = 98

Hence:  "none"

Hey, if it works, what the h**l!

Alan: That is nice, but sounds like "Voodoo Math"!!

BY PURE MAGIC!!.

I wish I knew!  Inspiration?!! (I.e. Lucky guess!)

Thanks, Alan.......your approach makes this much easier.......how did you happen to hit on that particular substitution????

Another approach:

Let y = z - 4 then we have:  (y + 1)^4 + (y - 1)^4  = -8

Expanding the terms in parentheses and collecting like terms:

2(y^4 + 6y^2 + 1) = -8 or:

y^4 + 6y^2 + 5 = 0

This factors nicely:  (y^2 + 1)((y^2 + 5) = 0

y^2 = -1  → y = i and y = -i.  Hence:  z = 4 + i and z = 4 - i

y^2 = -5  → y = i*sqrt(5) and y = -i*sqrt(5). Hence z = 4 + i*sqrt(5) and z = 4 - i*sqrt(5)

antilog [ (1.1129 ]  =  10^1.1129  =  about  12.9688

I am not sure what your real problem is,

inverse trig is the same as arc trig so on this calculator you use [2nd]  [asin] number      etc

Does that help or do you have a different problem ?

There are several but the one most used is :    Area  = [ triangle base * triangle height ]  / 2

Could you give us an example of what you're having trouble with???

Solve for z:
(z-5)^4+(z-3)^4 = -8

Expand out terms of the left hand side:
2 z^4-32 z^3+204 z^2-608 z+706 = -8

Add 8 to both sides:
2 z^4-32 z^3+204 z^2-608 z+714 = 0

The left hand side factors into a product with three terms:
2 (z^2-8 z+17) (z^2-8 z+21) = 0

Divide both sides by 2:
(z^2-8 z+17) (z^2-8 z+21) = 0

Split into two equations:
z^2-8 z+17 = 0 or z^2-8 z+21 = 0

Subtract 17 from both sides:
z^2-8 z = -17 or z^2-8 z+21 = 0

Add 16 to both sides:
z^2-8 z+16 = -1 or z^2-8 z+21 = 0

Write the left hand side as a square:
(z-4)^2 = -1 or z^2-8 z+21 = 0

Take the square root of both sides:
z-4 = i or z-4 = -i or z^2-8 z+21 = 0

Add 4 to both sides:
z = 4+i or z-4 = -i or z^2-8 z+21 = 0

Add 4 to both sides:
z = 4+i or z = 4-i or z^2-8 z+21 = 0

Subtract 21 from both sides:
z = 4+i or z = 4-i or z^2-8 z = -21

Add 16 to both sides:
z = 4+i or z = 4-i or z^2-8 z+16 = -5

Write the left hand side as a square:
z = 4+i or z = 4-i or (z-4)^2 = -5

Take the square root of both sides:
z = 4+i or z = 4-i or z-4 = i sqrt(5) or z-4 = -i sqrt(5)

Add 4 to both sides:
z = 4+i or z = 4-i or z = 4+i sqrt(5) or z-4 = -i sqrt(5)

Add 4 to both sides:
Answer: |z = 4+i   or   z = 4-i   or   z = 4+i sqrt(5)   or   z = 4-i sqrt(5)

(z-3)^4+(z-5)^4=-8   expanding, we have

z^4-12 z^3+54 z^2-108 z+81 + z^4-20 z^3+150 z^2-500 z+625  = - 8        simplify

2 z^4-32 z^3+204 z^2-608 z+714   = 0 

This will factor as :

2 (z^2-8 z+17) (z^2-8 z+21) = 0

Using the quadratic formula to solve the first quadratic factor, we have :

z = 4 - i

z = 4 + i

And using the quadratic formula to solve the second quadratic factor, we have

z =  4 - i sqrt(5) 

z =  4 + i sqrt(5)