To solve the equation [tex]\(3^{x+6} = 3^4\)[/tex], we notice that both sides of the equation have the same base (which is 3). When the bases are the same and the exponential expressions are equal, we can set the exponents equal to each other:
[tex]\[ x + 6 = 4 \][/tex]
Next, we need to solve for [tex]\(x\)[/tex]. To isolate [tex]\(x\)[/tex], we subtract 6 from both sides of the equation:
[tex]\[ x + 6 - 6 = 4 - 6 \][/tex]
[tex]\[ x = -2 \][/tex]
Therefore, the solution to the equation [tex]\(3^{x+6} = 3^4\)[/tex] is [tex]\(-2\)[/tex]. The correct answer is:
[tex]\[-2\][/tex]
