SOLUTION: Please help me to understand how to solve the equation: {{{ if 8^2n+1=2^n+18;n= }}} The answer for N is suppose to be 3. I cannot figure it out. ^2n+1 is the exponent for the

Algebra ->  Exponents -> SOLUTION: Please help me to understand how to solve the equation: {{{ if 8^2n+1=2^n+18;n= }}} The answer for N is suppose to be 3. I cannot figure it out. ^2n+1 is the exponent for the       Log On


   

Question 394670: Please help me to understand how to solve the equation:
+if+8%5E2n%2B1=2%5En%2B18%3Bn=+
The answer for N is suppose to be 3. I cannot figure it out. ^2n+1 is the exponent for the first half of the if statement. ^n+18 is the exponent for the second half of the if statement. If I substitute 3 for the N, is it 8 to the 23 power plus one power? or 8 to the second power times the third power plus one power. Anyway, does 8 to the 7th power = 2 to the 21 power?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
8%5E%282n%2B1%29=+2%5E%28n%2B18%29 ;n=
:
Since 8 can be written 2^3, we can write the equation
2%5E%283%282n%2B1%29%29=+2%5E%28n%2B18%29
which is:
2%5E%286n%2B3%29=+2%5E%28n%2B18%29
now since they have the same base we can ignore the base and write it
6n + 3 = n + 18
6n - n = 18 - 3
5n = 15
n = 15/5
n = 3
:
:
Check this in the original problem
8%5E%282%283%29%2B1%29=+2%5E%283%2B18%29
8%5E7=+2%5E21
a calc gives 2097152 for both sides