<s>[INST] Find the value of $x$ that satisfy the equation: $3^{11}+3^{11}+3^{11} = 3^x$ I have this question:


$$3^{11}+3^{11}+3^{11} = 3^x$$
    Find the value of $x$


 [/INST] Answer:


$$3^{11}+3^{11}+3^{11} = 3^x\implies 3^{10}(3^{1} + 3^{1} + 3^{1}) =3^x$$
    $$(3^1 + 3^1+ 3^1) = \frac {3^x} {3^{10}}$$
    $$9 = \frac{3^x}{3^{10}}$$
    $$3^2 = \frac {3^x}{3^{10}}$$
    Hence:
    $$2 = x -10$$
    $$x = 12$$


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