Question

Solve for x; 3 ^ (x + 2) + 3 ^ (x + 3) = 324
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Answer 1

Answer:

The answer is $x=2$

Step-by-step explanation:

Given equation is $\displaystyle 3^{x+2}+3^{x+3}=324$

                            $\Rightarrow \displaystyle 3^x\times 3^2+3^x\times 3^3=324$, since $a^{m+n}=a^m\times a^n$

                            $\Rightarrow \displaystyle 3^x(3^2+ 3^3)=324\\\Rightarrow 3^x(9+27)=324\\\Rightarrow 3^x(36)=324\\\\\Rightarrow 3^x=\frac{324}{36}=9=3^2\\\Rightarrow x=2$equating the powers as bases are same