# Worksheet: Converting Exponential Expressions to Logarithmic Form

In this worksheet, we will practice utilizing the relationship between logarithms and exponentials to convert an exponential expression to its logarithmic form.

**Q1: **

Express in logarithmic form.

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**Q4: **

Express in its equivalent logarithmic form.

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**Q5: **

Express in its equivalent logarithmic form.

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**Q6: **

Express in its equivalent logarithmic form.

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**Q7: **

Express in its equivalent logarithmic form.

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**Q8: **

Express in its equivalent logarithmic form.

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**Q9: **

Express in its equivalent logarithmic form.

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**Q10: **

Express in its equivalent logarithmic form.

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**Q11: **

Express in its equivalent logarithmic form.

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**Q14: **

The value of an antique painting increases every year. The painting is currently worth , and it is expected to be worth in 8 years’ time.

Write an equation that can be used to find , the rate at which its value increases.

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**Q16: **

The population of a rare orchid declines by every year. There are currently only 99 of these orchids left, and conservationists predict that only 50 will be left in 5 years. Write an equation that can be used to find , the rate of decline.

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**Q18: **

Find the solution set of and in .

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**Q19: **

Given that and , determine the value of .

**Q20: **

Find the solution set of in .

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**Q21: **

Given that , find .

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**Q22: **

Which of the following satisfies the equation ?

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**Q23: **

Determine the solution set of the equations and , given that it is a subset of .

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**Q24: **

Given that , determine the solution set of .

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**Q25: **

Find the solution set of and in .

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