Question

For what value of a does (1/7)^(3a+3)=343^(a-1)
​

Answer 1

a = 0

Explanation:

`\left((1)/(7)\right)^(3a+3)=343^(a-1)\qquad\text{use}\ a^(-n)=\left((1)/(a)\right)^n\\\\7^(-(3a+3))=(7^3)^(a-1)\qquad\text{use the distributive property}\\\\7^(-3a-3)=7^(3a-3)\iff-3a-3=3a-3\qquad\text{add 3 to both sides}\\\\-3a=3a\qquad\text{subtract}\ 3a\ \text{from both sides}\\\\-6a=0\qquad\text{divide both sides by (-6)}\\\\a=0`