MA-TEST in Exponential and Logarithmic Function

Michael is trying to solve a problem where the growth of a bacteria culture is modeled by the equation e^x = 9. Help Michael rewrite this equation using a logarithm.

• ln x = 9

• ln 9 = x

• log_x e = 9

• log₉ x = e

Noah is trying to determine the dimensions of a rectangular garden. The length of the garden is represented by ln3x and the width by ln2x. If the area of the garden is 3 square units, find the value of x. Round your solution to two decimal places.

• x = 12.91

• x = 4.02

• x = 3.35

• x = 1.83

Expand ln xy²z³

• 6(lnx + lny - lnz)
• lnx + 2lny - 3lnz
• lnx + (1/2)lny + (1/3)lnz
• lnx + 2lny + 3lnz

Aria is studying different types of logarithms in her math class. She learns that the log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

Evaluate.
log₇49 + log₂32 = ?

• log₉81
• log7
• 2
• 7

James is trying to solve a puzzle where he needs to find the base of a logarithm. The expression given to him is: log₇49 = 2. What is the base in this log expression?

• 7

• 49

• 2

• 7492

Evelyn is trying to solve a math problem where she needs to find the base in this log expression: log 100 = 2. Can you help her identify the base?

• 100

• 2

• 1002

• 10

Oliver is building a model of a pyramid for his school project. He knows that the base of the pyramid is a square with a side length of 6 units, and the height of the pyramid is 2 units. He wants to calculate the volume of the pyramid using the formula for the volume of a square pyramid, which involves an exponent. Change to Exponential Form:
log₆36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

• 0

• Undefined

• 17

• 1

Write 2³= 8 in logarithmic form.

• log₂ 8 = 3
• log₂ 3 = 8
• log₃ 8 = 2
• log₃ 2 = 8