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In this lesson, we will learn how to solve logarithmic equations using the laws of logarithms and the relationship between logarithmic and exponential functions.

Q1:

Determine the solution set of the equation l o g l o g l o g 8 8 8 ( π₯ β 6 ) + ( π₯ + 6 ) = 6 4 in β .

Q2:

Find π₯ such that l o g ( 4 π₯ β 4 ) = 2 .

Q3:

Solve the equation l o g οΉ π₯ β π₯ β 2 ο = 1 2 , where π₯ β β .

Q4:

Find the solution set of l o g l o g 6 6 ( β 2 π₯ + 4 8 ) = 2 π₯ in β .

Q5:

Solve l o g 4 2 π₯ β 2 6 π₯ β 7 π₯ + 6 = 1 , where π₯ β β .

Q6:

Find the solution set of οΊ π₯ ο + π₯ + 1 = οΊ 2 ο l o g l o g l o g 7 2 7 2 7 2 in β .

Q7:

Determine the solution set of the equation l o g l o g 2 2 π₯ = 4 β ( π₯ + 6 ) in β .

Q8:

Solve l o g l o g 2 3 2 οΊ οΉ π₯ β 8 π₯ ο ο = 1 , where π₯ β β .

Q9:

Find the solution set of 3 + 2 4 3 = 2 4 4 Γ 3 2 π₯ π₯ in β .

Q10:

Find the solution set of 4 + 2 = 5 1 6 π₯ π₯ + 8 in β .

Q11:

Find the solution set of 3 + 2 4 3 3 = 3 6 π₯ π₯ in β .

Q12:

What is the solution set of the equation l o g π₯ ( 9 π₯ β 1 8 ) = 2 ?

Q13:

Find the solution set of 4 β 1 0 2 6 Γ 2 + 2 0 4 8 = 0 π₯ + 8 π₯ + 8 2 2 in β .

Q14:

Find the solution set of l o g l o g l o g 6 2 6 6 οΉ 9 π₯ β 2 7 ο = 2 π₯ + 1 3 2 1 6 in β .

Q15:

Find the solution set of l o g l o g l o g l o g π₯ π₯ π₯ π₯ 5 + 4 0 β 2 4 = 2 + 8 in β .

Q16:

Determine the solution set of the equation 2 Γ 5 = 6 4 0 0 0 3 π₯ π₯ l o g l o g 3 3 in β .

Q17:

Find the solution set of l o g l o g π₯ 2 Γ 2 π₯ = β 4 in β .

Q18:

Determine π ( 2 4 3 ) , given that the graph of the function π ( π₯ ) = π₯ l o g π passes through the point ( 8 1 , 4 ) .

Q19:

Find the solution set of l o g l o g l o g l o g 9 9 9 9 6 2 1 6 Γ 8 1 = 3 6 Γ π₯ in β .

Q20:

Solve 5 = 1 5 l o g 6 π₯ , where π₯ β β .

Q21:

Solve l o g 2 π₯ ( 2 + 5 1 0 ) = 1 0 β π₯ , where π₯ β β .

Q22:

Determine the solution set of the equation l o g l o g 3 2 3 οΉ π₯ β 5 π₯ + 4 ο = 4 + ( π₯ β 1 ) in β .

Q23:

Solve the equation l o g π₯ 3 5 π₯ = 5 π₯ , where π₯ β β .

Q24:

If 8 π₯ + 5 π¦ β π₯ π¦ = 3 l o g l o g l o g 6 6 6 6 3 , what is the value of π₯ π¦ ?

Q25:

Determine the solution set of ο οΎ 5 0 3 + 3 ο = 8 l o g l o g 8 ο 8 β 3 π₯ 3 in β .

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