Practice Solving Exponential Equations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Solving exponential equations means finding the unknown variable trapped in an exponent by applying logarithms to both sides, using the power rule to bring the exponent down, and then isolating the variable with standard algebra.
When the variable is trapped in an exponent, logarithms free it. Taking \log of both sides brings the exponent down to ground level where you can solve for it using algebra.
Example 1
easySolve 3^x = 81.
Example 2
mediumSolve 5^{2x-1} = 12.
Example 3
mediumSolve 2^{x+3} = 7^{x-1}.
Example 4
hardSolve e^{2x} - 5e^x + 6 = 0.