Sidney P. answered • 05/23/20

Astronomy, Physics, Chemistry, and Math Tutor

In this case, you first divide both sides by a, so that 10^{mx} = c/a. Take common log of both sides: log(10^{mx}) = log (c/a). The logarithm of a power property states that log a^{b} = b log a, therefore we get (mx)log 10 = log (c/a). Now the common log base is 10, and log_{b} b = 1. Now it's simple algebra: mx = log (ca), and x = (log (c/a)) /m.