For the equation 27^x = 3^x+7, which of the following is the solution for x?

1. No solution
   Incorrect. You may consider getting the same base first.
2. x = 3.5
   Correct! You solved the equations correctly.
3. x = 7 4
   Incorrect. After setting exponents equal, subtract x from both sides to isolate variable.
4. x = 2
   Incorrect. Check solution.

Suzanne wants to solve the equation below by finding the same bases.

4^2x = 8^x-1

Which of the following could be the first step to solve this equation using the same bases?

1. 2^2x+2 = 2^x-1+2
   Incorrect. When raising a power to a power, multiply the exponents.
2. 8^4x = 8^x-1

   Incorrect. 4² ≠ 8²

3. 4^2x = 4^2(x-1)
   Incorrect. 4² ≠ 8
4. 2^4x = 2^3(x-1)
   Correct! You substituted 2² for 4 and 2³ for 8.

Roy needs help solving the equation below. He did the first step and then got stuck.

721 = 2^3x
log721 = log2^3x

Which of the following is the next step to solve the equation?

1. log 721 = (3x)log 2
   Correct! Since there was a power raised to a higher power, you multiplied.
2. log 721 = 21log 3x
   Incorrect. For a power to a power, multiply. This one transposed the numbers.
3. (3x)log 721 = log 2
   Incorrect. For a power to a power, multiply. This one multiplied 3x to the other side.
4. (2)log 721= log 3x
   Incorrect. For a power to a power, multiply. This one transposed the numbers and multiplied to wrong side.

For the equation 20,000 = 10,000(1.045)^t, which of the following is a solution for t?

1. t = 1.1
   Incorrect. Isolate the exponential term first.
2. t = 15.7
   Correct! You solved correctly.
3. t = 0.06
   Incorrect. To isolate variable, divide by coefficient.
4. t = 0.01
   Incorrect. To isolate variable, divide by coefficient.