Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve exponential equations of the form \(ae^(ct)=d\) by isolating the exponential factor and using natural logarithms
Problem
What is the solution to \(e^{2x}=7\) using natural logarithms?
Big Picture
What this problem is really about
Natural logarithms are the direct inverse tool for an exponential with base e. Apply the logarithm to both sides so the exponent becomes an ordinary linear expression, then divide by every coefficient still attached to the variable. Keeping the result exact also makes substitution especially clean.
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