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

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

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. An unknown liquid is tested and is found to have a hydrogen ion concentration of 10^-2. What is the pH?

Evaluate the expression.

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

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

Evaluate:

Find the height of an equilateral triangle with side 2 cm. (Use the Pythagorean theorem. Round the answer to 3 decimal places.)

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

What values of x would make this true?

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

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

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

Use scientific notation to perform each computation. Write your answers in scientific notation.

The time it takes for one complete swing of a pendulum is called the period of its motion. The period T (in seconds) of a swinging pendulum is found using the formula seconds where L is the length of the pendulum in feet and 32 is the acceleration of gravity in feet per second. Find the length of a pendulum whose period is 2.421 seconds. (Express the answer in feet and inches to the nearest inch.)

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

Express in meters, using powers of 10. 7.3 dekameters

What values of x would make this true?

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

Find the length of a side, s, of a cube with volume, V, of 343 in³. (Where V = s³.)

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