SOLUTION: Suppose that 3^(2x+1) = 12 Which of the following value is (1/81)^x ? a 1/4 b 1/8 c 1/16 d 1/32 e none of these

Algebra ->  Exponents -> SOLUTION: Suppose that 3^(2x+1) = 12 Which of the following value is (1/81)^x ? a 1/4 b 1/8 c 1/16 d 1/32 e none of these       Log On


   

Question 292930: Suppose that 3^(2x+1) = 12 Which of the following value is (1/81)^x ?
a 1/4 b 1/8 c 1/16 d 1/32 e none of these
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%282x%2B1%29=12 Start with the given equation.


3%5E%282x%29%2A3%5E1=12 Break up the exponent using the property x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez.


3%5E%282x%29%2A3=12 Simplify


3%5E%282x%29=12%2F3 Divide both sides by 3


3%5E%282x%29=4 Reduce.


%283%5Ex%29%5E2=4 Rewrite the left side using the identity x%5E%28yz%29=%28x%5Ey%29%5Ez


3%5Ex=sqrt%284%29 Take the square root of both sides.


3%5Ex=2 Take the square root of 4 to get 2.


%283%5Ex%29%5E%28-4%29=2%5E%28-4%29 Raise both sides to the -4th power


%283%5Ex%29%5E%28-4%29=1%2F16 Raise 2 to the -4th power to get 2%5E%28-4%29=1%2F2%5E4=1%2F16


3%5E%28-4x%29=1%2F16 Use the identity %28x%5Ey%29%5Ez=x%5E%28yz%29


1%2F%283%5E%284x%29%29=1%2F16 Rewrite 3%5E%28-4x%29 into 1%2F%283%5E%284x%29%29


1%2F%28%283%5E4%29%5Ex%29=1%2F16 Use the identity x%5E%28yz%29=%28x%5Ey%29%5Ez


1%2F%2881%5Ex%29=1%2F16 Raise 3 to the 4th power to get 81


%281%5Ex%29%2F%2881%5Ex%29=1%2F16 Rewrite 1 as 1%5Ex


%281%2F81%29%5Ex=1%2F16 Use the identity %28x%5Ez%29%2F%28y%5Ez%29=%28x%2Fy%29%5Ez


So the answer is %281%2F81%29%5Ex=1%2F16 which makes the answer C)


Note: Another way to do this problem is to explicitly solve for 'x' and plug that solution into %281%2F81%29%5Ex