solve: $7 + 42cdot3^{2 - 3a}=14cdot3^{-2a}+7$\n$a = - 3$\n$a = 0$\n$a = 3$\nno solution

Explanation:

Step1: Subtract 7 from both sides

$42\cdot3^{2 - 3a}=14\cdot3^{-2a}$

Step2: Divide both sides by 14

$3\cdot3^{2 - 3a}=3^{-2a}$

Step3: Use exponent - rule $a^m\cdot a^n=a^{m + n}$

$3^{1+2 - 3a}=3^{-2a}$ $3^{3 - 3a}=3^{-2a}$

Step4: Set the exponents equal

$3 - 3a=-2a$

Step5: Solve for a

$3=-2a + 3a$ $a = 3$

Answer:

$a = 3$