Learning Materials
Features
Discover
Chapter 12: Problem 36
Evaluate each expression without using a calculator. $$\log _{11} 11$$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Describe the relationship between an equation in logarithmic form and an equivalent equation in exponential form.
The pH scale is used to measure the acidity or alkalinity of a solution. The scale ranges from 0 to \(14 .\) A neutral solution, such as pure water, has a pH of 7. An acid solution has a pH less than 7 and an alkaline solution has a p \(H\) greater than \(7 .\) The lower the \(p H\) below \(7,\) the more acidic is the solution. Each whole-number decrease in \(p H\) represents a tenfold increase in acidity. The \(p H\) of a solution is given by $$\mathrm{pH}=-\log x$$ where \(x\) represents the concentration of the hydrogen ions in the solution, in moles per liter. Use the formula to solve. Express answers as powers of \(10 .\) a. Normal, unpolluted rain has a pH of about 5.6. What is the hydrogen ion concentration? b. An environmental concern involves the destructive effects of acid rain. The most acidic rainfall ever had a \(\mathrm{pH}\) of \(2.4 .\) What was the hydrogen ion concentration? c. How many times greater is the hydrogen ion concentration of the acidic rainfall in part (b) than the normal rainfall in part (a)?
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\ln \sqrt{2}=\frac{\ln 2}{2}$$
a. Simplify: \(e^{\ln 3}\) b. Use your simplification from part (a) to rewrite \(3^{x}\) in terms of base \(e\)
Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. \(\log _{3}(3 x-2)=2\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine