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For x > 0, a > 0, and a ≠ 1
Solving Exponential Equations –
An exponential equation is an equation with the variable in an exponent.
1. Isolate the exponential expression (the base and exponent).
Ex: 100 ×1.023x = 200 Divide both sides by 100
1.023x = 2
Ex: ln1.023x = ln2
3x ln1.02 = ln2
3. Solve for the variable and evaluate using a calculator
Solving Logarithmic Equations
2. Combine the terms with logarithms to get a single
logarithm with a coefficient
of 1 using properties 5, 6, and 7 (work from the right side to the left of each
3. Rewrite the equation in exponential form.
When checking, -6 does not give a solution since the
domain of all logarithmic
functions is x > 0. Therefore, the solution is x = 6.