Worksheet: Rearranging Formulas involving Logarithms

In this worksheet, we will practice rearranging formulas that contain logarithms and exponents.

Q1:

Which of the following algebraic expressions is a simpler form of 𝑝𝑒ln(), where 𝑝 and 𝑞 are variables?

  • A𝑝𝑞
  • B𝑝𝑞
  • C𝑝
  • D𝑝
  • E𝑝

Q2:

Which of the following algebraic expressions is a simpler form of 𝑟10log(), where 𝑟 and 𝑠 are variables?

  • A𝑟
  • B𝑟𝑠
  • C𝑠
  • D𝑟
  • E𝑟𝑠

Q3:

The quantities 𝑝, 𝑞, and 𝑟 are related to each other by the formula 𝑝=𝑞(𝑟)ln. Which of the following shows a rearrangement of this formula with 𝑟 as the subject?

  • A𝑟=𝑒
  • B𝑟=𝑒
  • C𝑟=𝑞𝑒
  • D𝑟=𝑝𝑞ln

Q4:

The quantities 𝑚, 𝑛, 𝑝, and 𝑞 are related to each other by the formula logloglog(𝑝)=(𝑚)(𝑛). Which of the following shows a rearrangement of this formula with 𝑞 as the subject?

  • A𝑞=(𝑚𝑛)(𝑝)loglog
  • B𝑞=(𝑝)loglog
  • C𝑞=𝑚𝑛𝑝
  • D𝑞=𝑚𝑛𝑝
  • E𝑞=(𝑒)log

Q5:

Which of the following algebraic expressions is a simpler form of 𝑎2log, where 𝑎 and 𝑏 are variables?

  • A𝑎𝑏
  • B𝑏𝑎
  • C𝑎
  • D𝑎𝑏
  • E𝑏

Q6:

The distance in parsecs, 𝑑, to a star can be calculated from the apparent magnitude of the star, 𝑚, and the absolute magnitude of the star, 𝑀, using the formula 𝑚𝑀=5𝑑10log. Which of the following shows a rearrangement of this formula with 𝑑 as the subject?

  • A𝑑=10×10
  • B𝑑=10
  • C𝑑=10×10
  • D𝑑=10×10()
  • E𝑑=10

Q7:

The quantities 𝐴, 𝐵, 𝐶, and 𝐷 are related to each other by the formula 𝐴+𝐵(𝐷)=𝐵(𝐶)lnln. Which of the following shows a rearrangement of this formula with 𝐶 as the subject?

  • A𝐶=𝐷𝑒
  • B𝐶=𝑒𝐷
  • C𝐶=𝑒𝐷
  • D𝐶=𝑒
  • E𝐶=𝐷𝑒

Q8:

For a capacitor that is discharging through a circuit that contains only a resistor, the charge, 𝑄, remaining on the capacitor at a time 𝑡 after the capacitor began discharging is given by 𝑄=𝑄𝑒, where 𝑄 is the charge on the capacitor when 𝑡=0, 𝑅 is the resistance of the resistor, and 𝐶 is the capacitance of the capacitor. Which of the following shows a rearrangement of this formula with 𝑡 as the subject?

  • A𝑡=1𝑅𝐶𝑄𝑄ln
  • B𝑡=𝑅𝐶𝑄𝑄ln
  • C𝑡=𝑅𝐶𝑄𝑄ln
  • D𝑡=𝑅𝐶𝑄𝑄ln
  • E𝑡=𝑅𝐶𝑄𝑄ln

Q9:

The quantities 𝑔, , and 𝑘 are related to each other by the formula 𝑔=×10. Which of the following shows a rearrangement of this formula with 𝑘 as the subject?

  • A𝑘=(𝑔)log
  • B𝑘=𝑔log
  • C𝑘=𝑔ln
  • D𝑘=𝑔log
  • E𝑘=𝑔ln

Q10:

The quantities 𝑎, 𝑏, 𝑐, and 𝑑 are related to each other by the formula 𝑎=𝑏(𝑐)+𝑏(𝑑)lnln. Which of the following shows a rearrangement of this formula with 𝑐 as the subject?

  • A𝑐=𝑒𝑑
  • B𝑐=𝑑𝑒
  • C𝑐=(𝑑)𝑒ln
  • D𝑐=𝑒𝑑
  • E𝑐=𝑒𝑑

Q11:

Which of the following algebraic expressions is a simpler form of 𝑎(𝑒)ln, where 𝑎 and 𝑏 are variables?

  • A𝑏𝑎
  • B𝑎𝑏
  • C𝑏
  • D𝑎𝑏
  • E𝑎

Q12:

The quantities 𝑎, 𝑏, and 𝑐 are related to each other by the formula 𝑎=𝑏𝑒. Which of the following shows a rearrangement of this formula with 𝑐 as the subject?

  • A𝑐=𝑒
  • B𝑐=(𝑎𝑏)ln
  • C𝑐=𝑏𝑎ln
  • D𝑐=𝑒
  • E𝑐=𝑎𝑏ln

Q13:

The quantities 𝑎, 𝑏, and 𝑐 are related to each other by the formula 𝑎=𝑏(𝑐)log. Which of the following shows a rearrangement of this formula with 𝑐 as the subject?

  • A𝑐=10
  • B𝑐=10
  • C𝑐=𝑒
  • D𝑐=𝑎𝑏log

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