Question 1 Report
Given that \(27^{(1+x)}=9,)\ find x
Answer Details
Taking the natural logarithm of both sides, we have: \begin{align*} \ln(27^{1+x}) &= \ln 9 \\ (1+x)\ln 27 &= \ln 9 \\ (1+x)\ln(3^3) &= \ln(3^2) \\ (1+x)(3\ln 3) &= 2\ln 3 \\ 1+x &= \frac{2\ln 3}{3\ln 3} \\ 1+x &= \frac{2}{3} \\ x &= \frac{2}{3} - 1 \\ x &= -\frac{1}{3} \end{align*} Therefore, the answer is (b) \(\frac{-1}{3}\).