Textbook Question
Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.
220
views
Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Chapter 5, Problem 7
Solve each equation. Round answers to the nearest hundredth as needed. (1/4)^x=64
Verified Solution
Video duration:
3m
This video solution was recommended by our tutors as helpful for the problem above.Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
5:47
Solving Exponential Equations Using Logs
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.
Recommended video:
7:30Logarithms Introduction
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.
Recommended video:
4:47The Number e
Related Practice
Textbook Question
Answer each of the following. Write log_3 12 in terms of natural logarithms using the change-of-base theorem.
236
views
Textbook Question
Answer each of the following. Between what two consecutive integers must log_2 12 lie?
369
views
Textbook Question
Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36
203
views
Textbook Question
Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4.
3^x = 7
220
views