Solve each equation. Round answers to the nearest hundredth as needed. (1/4)^x=64

Key Concepts

Exponential Equations

Exponential equations are equations in which variables appear as exponents. To solve these equations, one often needs to express both sides with the same base or use logarithms. In this case, the equation (1/4)^x = 64 can be transformed to find a common base or manipulated using logarithmic properties.

Logarithms

Logarithms are the inverse operations of exponentiation, allowing us to solve for the exponent in an equation. The logarithm of a number is the exponent to which a base must be raised to produce that number. For example, if we rewrite the equation using logarithms, we can isolate x and solve for its value.

Rounding Numbers

Rounding numbers involves adjusting a number to a specified degree of accuracy, often to simplify calculations or present results clearly. In this problem, rounding to the nearest hundredth means keeping two decimal places, which is important for providing a precise answer in a real-world context.