Grade 12 Advance Mathematics Question Paper 1 : Question 8

 To  solve the equation

$3^{𝑥+2}=\frac{1}{27}$, we begin by recognizing that $1\mathrm{/}27$ can be expressed as $3^{-3}$ because $3^{-3}=\frac{1}{3^3}=\frac{1}{27}$. This allows us to rewrite the equation as $3^{𝑥+2}=3^{-3}$.

Since both sides have the base 3, we can equate the exponents, resulting in $𝑥+2=-3$.

Then, by isolating $𝑥$, we subtract 2 from both sides to find $𝑥=-3-2$, simplifying to $𝑥=-5$.

Therefore, the solution to the equation is $𝑥=-5$.

Mathematical

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