Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. p = a + (k/ln x), for x

Key Concepts

Logarithms

Logarithms are the inverse operations of exponentiation, allowing us to solve equations where the variable is an exponent. They are defined as log_b(a) = c, meaning b^c = a. Understanding logarithms is essential for manipulating equations involving exponential growth or decay, particularly when isolating variables.

Natural Logarithm (ln)

The natural logarithm, denoted as ln, is a logarithm with base e (approximately 2.718). It is commonly used in calculus and algebra for solving equations involving exponential functions. In the context of the given equation, using ln helps to simplify the expression and isolate the variable x effectively.

Isolating Variables

Isolating a variable involves rearranging an equation to solve for that specific variable. This process often requires the use of algebraic operations such as addition, subtraction, multiplication, division, and logarithmic transformations. Mastery of this concept is crucial for solving equations like the one presented, where x needs to be expressed in terms of other variables.