# 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 , where and are variables?

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**Q2: **

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

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**Q3: **

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

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**Q4: **

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

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**Q5: **

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

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**Q6: **

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

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**Q7: **

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

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**Q8: **

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

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**Q9: **

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

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**Q10: **

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

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**Q11: **

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

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**Q12: **

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

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**Q13: **

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