Determine a value of x such that (5-3x)^5=-1.?

Question

Please show your work. Thanks =)

Answer 1

(5-3x)^5= -1 raise each side to the (1/5) power to get ((5-3x)^5)^1/5= (-1)^1/5 which is equal to 5-3x= -1 upon simplification. Subtract five from both sides to get -3x=-6. Divide both sides by -3 to get x=2.

Answer 2

Raise both sides to the 1/5 power. 5-3x = (-1) ^.2

5-3x = -1

-3x = -6

x = 2

Answer 3

If you are doing this at grade 9 (or so) level, then the other people who've answered this question have already supplied the answer. If you're doing it at grade 12 or uni level, then there's a bit more to it.

Let X = 5 - 3x, so we now need to solve X^5 = -1.
Because this is a quintic, it has 5 roots, and so we need 5 answers of which 2 is one.

-1 = ln (exp -1) where exp -1 means e^-1
= ln [(exp -1) (exp 2k pi i) ] where k is an integer
= ln (exp (2k pi i -1))
So X^5 = ln (exp ((2k pi i) -1))
Since a number equals the logarithm of its exponential and it also equals the exponential of its logarithm, it is also true that
X^5 = exp(ln ((2k pi i) -1))
Fifth rooting both sides gives
X = exp (ln ((2k pi i) -1)))/5
x = (5 - X)/3, so
x = [5 - exp (ln((2k pi i)-1)))/5]/3

Substitute k = 0, 1, 2, -1, -2 to get the 5 different answers.

Answer 4

I would say:
(5-3x)^5=-1 take the 5th root on each side
(5-3x)= -1 also because it's an odd power (5th)
5+1=3x
6=3x
2=x

Ok, so the tricky part was the 5th root thing.
See it this way:
sqrt(-1) wouldn't exist because nothing negatif multiplied by itself can result in a negative answer. (Actually, in electricity, we need the sqrt(-1) so thay named it simply i. But that's another story)

3rd root of (-1) would be -1 because (-1)x(-1)x(-1)=(-1) again.
4th root of (-1) wouldn't exist (or be i again)
5th root of (-1) would be -1 because (-1)x(-1)x(-1)x(-1)x(-1)=(-1)

and so on and so on.
So an even power would be a nonexistant answer (or a i one in electricity) and a odd power would be (-1).

Answer 5

first of all the inequalities could desire to be ? or ? considering that those have been interior the unique. as quickly as you discover the boundary factors (-a million/3 is the comparable as -3/9, only decreased), you are attempting factors on the two ingredient of the barriers interior the unique and notice in the event that they paintings. If x is to the left of -a million/3, say -a million : |-7| ? |a million| is fake If x is between -a million/3 and seven, say 0: |-2| ? |5| is actual If x is to the main dazzling of seven, say 8: |38| ? |37| is fake so in undemanding terms numbers between -a million/3 and seven worked making -a million/3 ? x ? 7

Answer 6

5-3x=2x
2x to the 5th power=32x
32x= -1
divide each side by 32 to isolate the variable
x=

Answer 7

Erm... fifth root (??? Is that how you called it?) both sides:
5 - 3x = (-1)^(1/5)
5 - 3x = -1
Add 1 and -3x to both sides:
5 + 1 = 3x
6 = 3x
x = 2

Hope this helps :)

Answer 8

you need to tell in which set is X ? is real ? complex ?

because I can take i^2=-1

So : (5-3x)^5=i^2

5-3x = i^(2/5)

x = [5-i^(2/5 )]/3