# How to solve: (11011)^2 = ( ? )^10?

Relevance
• 1 month ago

Given the pattern of the number (11011) using only the digits 0 and 1, it appears you were trying to show a base 2 number. But you used the ^ symbol which is understood to be an *exponent*, not a base.

I'm going to assume you are asking how to convert 11011₂ to a number in base 10.

An easy way to convert the number to base 10 is to write each place value over the digits. On the far right, start with 1, then double to 2, then 4, then 8 and finally 16:

16 8 4 2 1

--------------

.1 .1 0 1 1

We add up the place values with ones and ignore the place value with a 0:

16 + 8 + 2 + 1

= 27

Another common method is to work left to right. Add the first digit, then double and add the next digit, etc.

1

1*2 = 2 --> + 1 = 3

3*2 = 6 --> + 0 = 6

6*2 = 12 --> + 1 = 13

13*2 = 26 --> + 1 = 27

11011₂ = 27₁₀

P.S. It's confusing if you use ^ to mean a base. That's understood to mean an exponent. If you can't type a subscript, you could use an underscore, but that may not be universally understood either.

11011_2 = 27_10

Or you could just write:

11011 (base 2) = 27 (base 10)

• 1 month ago

11011^(2) = x^(10)

x^(10) = 11011^(2)

[x^(10)]^(1/10) = [11011^(2)]^(1/10)

x^[10 * (1/10)] = 11011^[2 * (1/10)]

x^(10/10) = 11011^(2/10)

x = 11011^(1/5)

• 1 month ago

Let the unknown number (?) = a

Then  (11011)² = (x)^10

=> 10 log (x) =  2 log (11011)

=> log (x)^5  =  log (11011)

=> x^5  =  (11011)

=>  x = (11011)^(1/5) = ± 6.43228

Unknown number  =  ± 6.43228  ....................... Answer

• 1 month ago

If 11011 is in the base of 10 then let

x^10=11011

=>

10ln(x)=ln(11011)

=>

ln(x)=0.930665005

=>

x=2.5361952

Check: 2.5361952^10=11011 valid.

If you want to convert 11011 in the base of 2 to some thing

in the base of 10, then

• 1 month ago

11011^2 = x^10

x^10 = 121242121

2 real solutions, 8 non-real solutions.

https://www.wolframalpha.com/input/?i=%2811011%29%...

• 1 month ago

11011^2 = x^10

Take the 10th root of both sides.

(11011^2)^(1/10) = (x^10)^(1/10)

simplify

11011^(1/5) = |x|

x = ± 11011^(1/5)

or as an approximate decimal answer

x = ± 6.4323

• Jim
Lv 7
1 month ago

11011^(1/5) = 6.4322860923706519418441410883209

11011 has 5 sigfigs

Round answer to 5 digits as well: 6.4323

• 1 month ago

11011^2 = x^10 = (x^5)^2

11011 = x^5

x = 5th root of 11011 or 11011^(1/5)

x = 6.432286

Verify:

6.432286^10 = 121242104

sqrt(121242104) = 11011

• fcas80
Lv 7
1 month ago

I'm assuming 11011 is base ten because you didn't say otherwise.

(11011)^2 = ( x )^10

LN(11011)^2 = LN( x )^10

2LN(11011) = 10LN(x)

1.86133 = LN(x)

e^1.86133 = x

6.43229 = x

• 1 month ago

(11011)^2 = x^10

log base 10 both sides

log (x¹⁰) = log (11011²)

10 log x = 2 log 11011

log x = (1/5) log 11011

x = 10^((1/5) log 11011)

x = (10^log 11011)^(1/5)

x = 11011^(1/5)

alternative

(you could use any log, ans would be the same)

(11011)^2 = x^10

log e both sides

ln (x¹⁰) = ln (11011²)

10 ln x = 2 ln 11011

ln x = (1/5) ln 11011

x = e^((1/5) ln 11011)

x = 11011^(1/5)

if you want a numerical ans

x = 11011^(1/5)

x = 6.432286