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In this lesson, we will learn how to use logarithms to solve exponential equations.

Q1:

Use a calculator to find the value of π₯ for which 2 = 3 π₯ . Give your answer correct to two decimal places.

Q2:

Use a calculator to find the value of π₯ for which 3 = 1 3 π₯ . Give your answer correct to two decimal places.

Q3:

Use a calculator to find the value of π₯ for which 9 = 8 π₯ . Give your answer correct to two decimal places.

Q4:

Find, to the nearest hundredth, the value of π₯ for which 2 = 9 π₯ + 8 .

Q5:

Find the solution set of 8 + 8 = 6 5 2 β π₯ β π₯ in β .

Q6:

Find the solution set of π₯ = 1 0 l o g π₯ 6 π₯ 6 4 l o g in β .

Q7:

Find the solution set of 4 = π₯ π₯ + 3 π₯ + 3 in β .

Q8:

Determine the solution set of the equation 4 = 8 l o g l o g π₯ 4 in β .

Q9:

Given that 5 = 2 π₯ , determine the value of 2 5 π₯ .

Q10:

Use a calculator to find the value of π₯ for which 2 Γ· 5 = 2 2 β 5 π₯ π₯ + 3 . Give your answer correct to two decimal places.

Q11:

The variables π , π , π , π a n d are related by the formula π = π ( π β 1 ) π β 1 π , where π = 1 4 4 , π = 3 2 , and π = 1 . 8 9 9 Γ 1 0 3 . Find π .

Q12:

Find all the values of π₯ in β which satisfy π₯ = 1 0 π₯ + 6 π₯ + 6 .

Q13:

What is the π₯ -coordinate of the point where the graphs of π ( π₯ ) = 9 π₯ β 2 0 and π ( π₯ ) = 6 π₯ β 2 0 intersect?

Q14:

Determine the solution set of ( π₯ β 2 ) = 1 π₯ β 1 2 .

Q15:

Given that 9 = 8 4 π β 4 8 4 π β 4 8 , where π β β€ , determine the value of π .

Q16:

Use a calculator to find the value of π₯ for which π₯ = 9 7 . 4 7 . 1 . Give your answer correct to two decimal places.

Q17:

Find the value of π₯ for which 3 6 = 2 3 π₯ . Give your answer to the nearest hundredth.

Q18:

Find the value of π₯ for which 8 = 1 2 . 7 3 β 2 π₯ . Give your answer to the nearest tenth.

Q19:

Given that 2 = 1 8 π₯ and π < π₯ < π + 1 , where π is an integer, determine the value of π .

Q20:

If 6 = 9 π₯ , what is the value of 3 6 π₯ ?

Q21:

Find the solution set of 8 = 9 π₯ β 7 π₯ β 7 in β .

Q22:

Find the solution set of 7 Γ 5 = 1 7 π₯ β 5 1 5 β 2 1 π₯ in β .

Q23:

Use a calculator to find the value of π₯ for which 3 = 8 β 4 π₯ β 3 π₯ + 4 . 7 . Give your answer correct to two decimal places.

Q24:

Find the solution set to the equation . Give your answer to three decimal places.

Q25:

Solve 2 β 3 = 5 β 4 π₯ π₯ for π₯ , giving your answer to three decimal places.

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