Cambridge O Level Additional Mathematics · Syllabus 4037 · Logarithmic and Exponential Functions
Exponential Equation
What is Exponential Equation?
An equation in which the unknown appears in an exponent, such as a raised to the power x equals b, where the base a is positive and not equal to one and b is strictly positive. Because the exponential function is one-one, such an equation has exactly one solution, given exactly by x equals the natural logarithm of b divided by the natural logarithm of a, which is the same as log to base a of b. If both sides can be rewritten as powers of a single common base, the exponents may instead be equated directly, which is usually faster and avoids logarithms altogether. If b is zero or negative there is no solution, because a positive base raised to any real power is positive.
This definition is part of the Logarithmic and Exponential Functions chapter in Cambridge O Level Additional Mathematics.