Exam 4: The Laws of Exponents and Logarithms: Measuring the Universe

Express as a power of 10.

Simplify the expression.

Simplify the expression. Express your answer using only positive exponents.

Simplify the expression. Express your answer using only positive exponents and evaluate whenever possible.

Which of the following statements is equivalent to ?

Rewrite in an equivalent form using logarithms: 10⁸ = 100,000,000

Simplify the expression. Express your answer using only positive exponents.

Convert to scientific notation. -7,050,000

The pH scale measures the hydrogen ion concentration in a liquid, which determines whether the substance is acidic or alkaline. A strong acid solution has a hydrogen ion concentration of 10^-1 M and would have a pH of 1. A neutral substance has a hydrogen ion concentration of 10^-7 M and would have a pH of 7. How many orders of magnitude more hydrogen ions does a substance with a pH of 3.7 have than a substance with a pH of 5.7?

Simplify the expression. Express your answer using only positive exponents.

Simplify the expression. Express your answer using only positive exponents.

Perform the conversion given the following information. 1 km = 0.6214 miles 1 gal = 0.13368 ft³ 1 cm³ = 3.53 x 10^-5 ft³ 1 cm³ = 10^-3 liters Convert 60 kilometers per liter to miles per gallon. If necessary, round your answer to 2 decimal places.

One earthquake has a Richter number of 5.1. A second has a Richter number of 8.1. How many times more intense is the second than the first?

The distance from Earth to the planet Pluto is miles. If a spaceship leaves from Earth travelling at a rate of 15,000 miles per hour, how many years will it take to reach Pluto? Round your answer to 2 decimal places. (Use 365 days in a year.)

Simplify the expression. Express your answer using only positive exponents and evaluate whenever possible.

Simplify the expression. Express your answer using only positive exponents.

Evaluate the expression.

How many orders of magnitude larger is a ton compared to a gram?

The atomic mass of an atom can be found by dividing the molar mass of the atom by Avogadro's number . The molar mass of hydrogen is 1.00797 g/mol. Find the mass of an atom of hydrogen. Express the answer in scientific notation.

Simplify the expression.