-------------------------------------------------------
answers:
MathLover say: Express 8 in 2^3 and 16 in 2^4 so that 2^3n = 2^4.4 so 3n = 16. n = 16/3
-
Nzewi Ernest Kenechukwu say: 8^n = 16^4
=> Express 8 and 16 in index form, and you'll have
(2^3)^n = (2^4)^4
2^(3n) = 2^16
=> By canceling the Base integer '2' from both sides, we have
3n = 16
Therefore, n = 16/3 ...Ans.
-
Johnathan say: 8^n = 16^4
(2^3)^n = (2^4)^4
2^(3n) = 2^16
3n = 16
n = 16/3.
-
Mathias say: 8^n = 16^4.
8^n = (8 * 2)^4.
8^n = 8^4 * 2^4.
8^n = (2^3)^4 * 2^4.
(2^3)^n = 2^(3 * 4) * 2^4.
2^(3n) = 2^12 * 2^4.
2^(3n) = 2^(12 + 4).
2^3n = 2^16.
---> 3n = 16.
Hence: n = 16/3.
Ans.: n = 16/3.
-
Krishnamurthy say: 8^n = 16^4
2^(3n) = 2^16
n = 5 1/3
-
la console say: 8^(n) = 16^(4) β you know that: 8 = 2^(3)
[2^(3)]^(n) = 16^(4) β you know that: 16 = 2^(4)
[2^(3)]^(n) = [2^(4)]^(4) β recall: (x^a)^b = x^(ab)
2^(3n) = 2^(16)
3n = 16
n = 16/3
-
Sadil say: Thanx Michael,,,
8^n = 16^4
=> (2^3)^n = (2^4)^4
=> 3*n = 4*4
=> 3n = 16
=> n = 16/3
=> n = 5.33333333
=> round-up n = 5.33
-
Tyler say: Take ln of each side
ln(8^n) = ln(16^4)
"Pull out the exponents" and place them as multiples in front of the natural logarithms:
n * ln(8) = 4*ln(16)
n = 4 ln(16)/ln(8)
n = 16/3
You may check to ensure it is right by plugging n in the original equation. You will see they're correct:
8^(16/3) = 2^16 = 16^4
16^4 = (2^4)^4 = 2^16
And so 2^16 = 2^16
A second way (if you can notice the pattern), would be to take the log_2() of each side, since 8 is 2^3 and 16 is 2^4
This would make it:
nlog_2(8) = 4log_2(16)
n * 3 = 4 * 4
n = 16 / 3
Same result, however ln is the more "general" form for solving this and doesn't require you to know that a certain number has a similar base of the other.
-
Michael say: Well,
8^x = 16^4
then
(2^3)^x = (2^4)^4
2^(3 * x) = 2^(4 * 4)
2^(3x) = 2^16
3x = 16
x = 16/3
qed
hope it' ll help !!
-
cidyah say: 8^n = 16^4
n log(8) = 4 log(16)
n log(2^3) = 4 log(2^4)
n (3 log(2)) = 4 ( 4 log(2) )
3n log(2) = 16 log(2)
3n= 16
n = 16/3
-