Lesson Worksheet: Rearranging Formulas involving Logarithms Physics • 9th Grade

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 π‘ž are variables?

  • Aπ‘π‘ž
  • Bπ‘π‘ž
  • Cο‘†βˆšπ‘
  • Dπ‘οŠ±ο
  • E𝑝

Q2:

Which of the following algebraic expressions is a simpler form of π‘Ÿ10log(), where π‘Ÿ and 𝑠 are variables?

  • Aπ‘Ÿο
  • Bπ‘Ÿπ‘ 
  • Cο‘‡βˆšπ‘ 
  • Dπ‘ŸοŠ±ο
  • Eπ‘Ÿπ‘ 

Q3:

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

  • Aπ‘Ÿ=𝑒
  • Bπ‘Ÿ=𝑒
  • Cπ‘Ÿ=π‘žπ‘’οŒ
  • Dπ‘Ÿ=ο€½π‘π‘žο‰ln

Q4:

The distance in parsecs, 𝑑, to a star can be calculated from the apparent magnitude of the star, π‘š, and the absolute magnitude of the star, 𝑀, using the formula π‘šβˆ’π‘€=5𝑑10log. Which of the following shows a rearrangement of this formula with 𝑑 as the subject?

  • A𝑑=10Γ—10ο‘‚οŽͺο₯
  • B𝑑=10ο‘‚οŽͺο₯
  • C𝑑=10Γ—10ο‰οŠ±οŒ¬
  • D𝑑=10Γ—10(ο‰οŠ±οŒ¬)
  • E𝑑=10ο₯οŽͺο‘‚οŽ€

Q5:

Which of the following algebraic expressions is a simpler form of π‘Žο€Ή2log, where π‘Ž and 𝑏 are variables?

  • Aπ‘Žπ‘
  • Bπ‘π‘Ž
  • Cπ‘ŽοŒ»
  • Dπ‘Žπ‘
  • Eπ‘οŒΊ

Q6:

The quantities π‘š, 𝑛, 𝑝, and π‘ž are related to each other by the formula logloglog(𝑝)=(π‘š)βˆ’(𝑛). Which of the following shows a rearrangement of this formula with π‘ž as the subject?

  • Aπ‘ž=(π‘šβˆ’π‘›)(𝑝)loglog
  • Bπ‘ž=(𝑝)loglogοŠ§οŠ¦ο‰οŠοŠ§οŠ¦
  • Cπ‘ž=π‘šπ‘›π‘
  • Dπ‘ž=π‘šβˆ’π‘›π‘
  • Eπ‘ž=(𝑒)logοŒο‰οŠ±οŠ

Q7:

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

  • A𝐢=βˆ’π·π‘’ο™οš
  • B𝐢=βˆ’π‘’π·ο™οš
  • C𝐢=π‘’π·ο™οš
  • D𝐢=π‘’οšο™οœ
  • E𝐢=π·π‘’ο™οš

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 𝑑 after the capacitor began discharging is given by 𝑄=π‘„π‘’οŠ¦οŠ±ο‘‰οͺ, where π‘„οŠ¦ is the charge on the capacitor when 𝑑=0, 𝑅 is the resistance of the resistor, and 𝐢 is the capacitance of the capacitor. Which of the following shows a rearrangement of this formula with 𝑑 as the subject?

  • A𝑑=βˆ’1𝑅𝐢𝑄𝑄ln
  • B𝑑=𝑅𝐢𝑄𝑄ln
  • C𝑑=𝑅𝐢𝑄𝑄ln
  • D𝑑=βˆ’π‘…πΆπ‘„π‘„ln
  • E𝑑=βˆ’π‘…πΆπ‘„π‘„ln

Q9:

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

  • Aπ‘π‘Ž
  • Bπ‘Žπ‘
  • Cπ‘οŒΊ
  • Dπ‘Žπ‘
  • Eπ‘ŽοŒ»

Q10:

The quantities π‘Ž, 𝑏, 𝑐, and 𝑑 are related to each other by the formula π‘Ž=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=π‘’π‘‘οŒΊοŠ±οŒ»

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