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In this lesson, we will learn how to utilize the relationship between logarithms and exponentials to convert an exponential expression to its logarithmic form.

Q1:

Express 4 = 1 0 in logarithmic form.

Q2:

Express 9 7 = 8 1 4 9 2 in its equivalent logarithmic form.

Q3:

Express 3 4 3 8 = 7 2 1 3 in its equivalent logarithmic form.

Q4:

Express 2 4 3 = 3 1 5 in its equivalent logarithmic form.

Q5:

Express 4 = 1 1 6 − 2 in its equivalent logarithmic form.

Q6:

Express ( 0 . 7 ) = 0 . 3 4 3 3 in its equivalent logarithmic form.

Q7:

Express ( 0 . 1 6 ) = 0 . 4 1 2 in its equivalent logarithmic form.

Q8:

Express 2 = 4 √ 2 5 2 in its equivalent logarithmic form.

Q9:

Express 1 0 = 1 0 0 0 3 in its equivalent logarithmic form.

Q10:

Express 2 = 1 1 6 √ 2 − 9 2 in its equivalent logarithmic form.

Q11:

Express √ 2 = 5 1 2 1 8 in its equivalent logarithmic form.

Q12:

Solve for 𝑥 2 = 3 : .

Q13:

Given that 2 − 6 = 1 0 4 𝑥 , find the value of 𝑥 .

Q14:

The value of an antique painting increases every year. The painting is currently worth $ 1 2 0 0 0 , and it is expected to be worth $ 2 0 0 0 0 in 8 years’ time.

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

Q15:

Solve for 𝑥 2 = 1 2 : 𝑥 + 5 .

Q16:

The population of a rare orchid declines by 𝑟 % 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 𝑟 , the rate of decline.

Q17:

Solve 1 8 = 6 4 𝑥 .

Q18:

Find the solution set of l o g l o g 2 2 𝑥 𝑦 = 5 − 4 and l o g l o g 2 1 0 2 𝑦 = 1 0 − 1 in ℝ × ℝ .

Q19:

Given that 4 = 3 𝑥 and 3 = 6 4 𝑦 , determine the value of 𝑥 𝑦 .

Q20:

Find the solution set of 9 = 1 7 2 9 𝑥 − 4 0 𝑥 2 in ℝ .

Q21:

Given that 7 6 × 𝑥 = 7 6 2 8 3 5 , find 𝑥 .

Q22:

Which of the following satisfies the equation 6 × 6 × 3 × 3 × 3 × 3 = 9 × 𝑥 ?

Q23:

Determine the solution set of the equations 𝑥 = 7 𝑥 + 6 𝑦 and l o g 𝑥 2 7 = 𝑦 , given that it is a subset of ℝ × ℝ .

Q24:

Given that 𝑓 ( 𝑥 ) = 2 𝑥 , determine the solution set of 𝑓 ( 𝑥 ) − 2 4 𝑓 𝑥 2 = − 1 2 8 .

Q25:

Find the solution set of l o g l o g l o g l o g 2 2 2 2 𝑥 + 𝑦 + 3 2 = 5 + 4 8 and 𝑥 + 𝑦 = 1 4 in ℝ × ℝ .

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