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In this lesson, we will learn how to express an exponential equation in logarithmic form, and vice versa, and how to evaluate logarithms with various bases.

Q1:

Express 2 = 2 5 6 8 in its equivalent logarithmic form.

Q2:

What is the value of l o g l o g 2 2 6 4 8 ?

Q3:

Find l o g 9 7 2 9 .

Q4:

If 3 = 2 4 π₯ , what is the value of π₯ ?

Q5:

Find the solution set of the equation l o g π₯ 3 4 3 = 3 in β .

Q6:

Find the solution set of the equation l o g 3 π₯ = β 2 in β .

Q7:

Find the value of l o g 4 2 2 . 0 8 correct to 4 decimal places.

Q8:

Use a calculator to find the number of digits of the number 3 8 7 .

Q9:

Triangle π΄ π΅ πΆ is right-angled at π΄ . Find its area, given that π΄ π΅ = 4 9 l o g c m 2 and π΄ πΆ = 5 1 2 l o g c m 7 .

Q10:

Find the values of l o g 1 4 1 9 6 and l o g 8 6 4 respectively.

Q11:

Use a calculator to find the value of l o g 5 3 . Give your answer correct to four decimal places.

Q12:

Since β 1 0 β 3 . 1 6 , what can we conclude about l o g ( 3 ) ?

Q13:

Find the value of 7 ( 1 5 . 6 2 ) β 8 ( 2 0 . 9 5 ) l o g l o g 9 correct to 4 decimal places.

Q14:

Given that l o g 4 5 4 6 = π and l o g 5 . 8 6 = π , find the value of 6 π π + 1 . Give your answer correct to four decimal places.

Q15:

Given that π β ο 0 , π 2 ο , evaluate l o g s i n l o g c s c ( π ) + ( π ) .

Q16:

Simplify l o g π₯ 4 6 β π₯ .

Q17:

Find the value of the number shown with the dot on the given logarithmic scale. Round your answer to the nearest thousandth.

Q18:

What is the value of l o g 2 οΏ 1 4 β 2 ο ?

Q19:

What is the value of l o g 0 . 1 ?

Q20:

What is the value of l o g 2 5 β 6 4 ?

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