Question

Guess an integer approximation to the solution of the following equation, indicating your reasoning, and then use logarithms to find the solution (accurate to 3 significant figures): 3^(x−1) = 28.

Answer 1

i know \(3^3=3\times3\times3=27\)
so \(x\) is probably a bit over 4

\[3^{x-1}=28\]\[x-1=\log_328=\frac{\log 28}{\log 3}\]\[x-1\approx3.033\]\[x\approx 4.033\]

Answer 2

so \(x=4.03\) to 3sig.figs.

Answer 3

THANK YOU!