Discussion
If \(\left(\frac{60}{7}\right)^{x-2} = \left(\frac{7}{60}\right)^{x-6}\), then x is equal to
Answer: B
x is equal to 4.
Turn the right-hand side into the same base by flipping the fraction, which changes the sign of the power:
\[ \begin{aligned} \left(\frac{7}{60}\right)^{x-6} &= \left(\frac{60}{7}\right)^{6-x} \\ x - 2 &= 6 - x \\ 2x &= 8,\ x = 4 \end{aligned} \]
Check: with \(x = 4\) the left side is \(\left(\frac{60}{7}\right)^{2}\) and the right side is \(\left(\frac{7}{60}\right)^{-2}\), which is the same number. Equating \(x - 2\) with \(x - 6\) directly, without flipping, has no solution, which is the trap.
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