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

Calculate:

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

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

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

Simplify and express the answer as a power of 10 with a positive exponent.

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

A period is the time it takes for one complete swing of a pendulum. The period T (in seconds) of a swinging pendulum is found using the formula where L is the length of the pendulum in feet. A) Find the period (in seconds) of a pendulum whose length is 2 feet 1 inches. B) How long (in inches) would a pendulum have to be to have a period of 6 seconds?Round answers to 2 decimal places.

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

Solve for x: Round the answer to 4 decimal places.

Express in meters, using powers of 10. 8.1 micrometers

Evaluate:

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

What values of x would make this true?

Solve for x: 10^x = 318,455.59 Round the answer to 4 decimal places.

Evaluate exactly.

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

Simplify and express the answer as a power of 10 with a positive exponent.

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

Solve. Round your answer to 3 decimal places.