Which of the following equations can be rewritten to have common bases on both sides? Select all that apply.(1 point) Responses 3x=4x+1 3 to the x th power is equal to 4 raised to the x plus 1 power 3x=92x−1 3 to the x th power is equal to 9 raised to the 2 x minus 1 power 43x−1=64x 4 raised to the 3 x minus 1 power is equal to 64 to the x th power 2x=6 2 to the x th power is equal to 6 81=9x 81 is equal to 9 to the x th power

Answer 1

To determine which equations can be rewritten to have common bases on both sides, let's analyze each option:

1. 3^x = 4^(x + 1)

   • Bases are not the same and cannot be converted to a common base.
   • Not applicable.

2. 3^x = 9^(2x - 1)

   • 9 can be expressed as \(3^2\), thus \(9^{2x - 1} = (3^2)^{2x - 1} = 3^{4x - 2}\).
   • This can be rewritten as \(3^x = 3^{4x - 2}\), which gives a common base (3) on both sides.
   • Applicable.

3. 4^(3x - 1) = 64^x

   • 64 can be expressed as \(4^3\), thus \(64^x = (4^3)^x = 4^{3x}\).
   • This can be rewritten as \(4^{3x - 1} = 4^{3x}\), which gives a common base (4) on both sides.
   • Applicable.

4. 2^x = 6

   • The left side is base 2 and the right side is base 6. These bases cannot be made common.
   • Not applicable.

5. 81 = 9^x

   • 81 can be expressed as \(9^2\), so this can be rewritten as \(9^2 = 9^x\), which gives a common base (9) on both sides.
   • Applicable.

In summary, the equations that can be rewritten to have common bases on both sides are:

• 3^x = 9^(2x - 1) (Applicable)
• 4^(3x - 1) = 64^x (Applicable)
• 81 = 9^x (Applicable)