2 Solving Exponential Functions with Logarithms There are three main steps to solving exponential functions using logarithms.Express each side of the equation as a single term.Take the logarithm of both sides, choosing a convenient base.Solve the resulting equation.
4 Solution: Step 1Conveniently, each side is already expressed as a single term. We can simplify the left side, though, by noticing that 4 = 22, so 4 * 2x-3 is equal to 2x-1.This simplifies our equation to 2x-1 = 5 * 3x
5 Solution: Step 2 Now we take the logarithm of both sides. Each side has a different base, so there’s no truly convenient base for us to use.We’ll use the natural log.ln(2x-1) = ln(5 * 3x)Now we can solve the equation using the properties of logarithms.
6 Solution: Step 3 ln(2x-1) = ln(5 * 3x) (x-1)ln(2) = ln(5) + xln(3) (ln(2) – ln(3))x = ln 5 + ln 2Using a calculator, we can calculate all of these natural logs.