In Exercises 101–104, write each equation in its equivalent exponential form. Then solve for x. log4 x=-3

Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions. The logarithm log_b(a) answers the question: 'To what exponent must the base b be raised to produce a?' In this case, log4(x) = -3 means that 4 raised to the power of -3 equals x. Understanding this relationship is crucial for converting between logarithmic and exponential forms.

Exponential Form

Exponential form expresses a logarithmic equation in terms of exponents. For the equation log_b(a) = c, the equivalent exponential form is b^c = a. This transformation is essential for solving logarithmic equations, as it allows us to isolate the variable and find its value, which is the goal in the given problem.

Solving Exponential Equations

Solving exponential equations involves isolating the variable and determining its value. Once the equation is in exponential form, we can manipulate it using properties of exponents. In this case, after converting log4(x) = -3 to its exponential form, we can solve for x by calculating 4 raised to the power of -3, which simplifies the process of finding the solution.