Lesson Worksheet: Logarithmic Equations with Different Bases Mathematics

In this worksheet, we will practice solving logarithmic equations involving logarithms with different bases.

Q1:

Find the solution set of loglog𝑥=4 in ℝ.

  • A{3}
  • B{2}
  • C{4}
  • D{5}

Q2:

Find the solution set of loglog𝑥+92=6 in ℝ.

  • A{3}
  • B{8}
  • C{2}
  • D{4}

Q3:

Determine the solution set of the equation loglog𝑥+254=10 in ℝ.

  • A{20}
  • B{10}
  • C{1,024}
  • D{9}
  • E{5}

Q4:

Solve loglog𝑥=149, where 𝑥∈ℝ.

  • A2
  • B−4
  • C14
  • D−14
  • E4

Q5:

Determine the solution set of the equation loglog𝑥+𝑥+3=0 in ℝ.

  • A{27}
  • B127
  • C3√3
  • D13√3

Q6:

Find the solution set of loglog𝑥=(3𝑥+28) in ℝ.

  • A{4}
  • B{7}
  • C{11}
  • D{128}
  • E{64}

Q7:

Find the solution set of loglog𝑥−49=−1 in ℝ.

  • A{1,−2}
  • B{14}
  • C7,149
  • D{1}

Q8:

Find the solution set of loglog𝑥=729 in ℝ.

  • A{81}
  • B{5}
  • C{9}
  • D{729}
  • E{14}

Q9:

Find the solution set of loglog𝑥+254=10 in ℝ.

  • A{5}
  • B{1,024}
  • C{4}
  • D{256}

Q10:

Find the solution set of loglog𝑥+252=10 in ℝ.

  • A{5}
  • B{32}
  • C{2}
  • D{16}

Q11:

Solve loglog𝑥=64, where 𝑥∈ℝ.

  • A81
  • B27
  • C729
  • D127
  • E1729

Q12:

Solve loglog𝑥−8𝑥=1, where 𝑥∈ℝ.

  • A{−2,27}
  • B{2,3}
  • C{−9,1}
  • D{−8,8}
  • E{−1,9}

Q13:

Solve loglog251+(𝑥+7)=8, where 𝑥∈ℝ.

Q14:

Solve loglog(7𝑥+194)=1, where 𝑥∈ℝ.

  • A𝑥=7
  • B𝑥=49
  • C𝑥=187
  • D𝑥=5

Q15:

Solve loglog𝑥+39=1, where 𝑥∈ℝ.

  • A𝑥=5 or 𝑥=−5
  • B𝑥=34 or 𝑥=−34
  • C𝑥=25 or 𝑥=−25
  • D𝑥=60 or 𝑥=−60
  • E𝑥=20 or 𝑥=−20

Q16:

Solve logloglog36=0, where 𝑥∈ℝ.

Q17:

Find the solution set of 𝑥=10loglog in ℝ.

  • A{2}
  • B{64}
  • C{32}
  • D{6}

Q18:

Find the solution set of 1𝑥−1𝑥=4logloglog in ℝ.

  • A{18}
  • B{16}
  • C{8}
  • D{6}
  • E{9}

Q19:

Find the solution set of logloglog𝑥+𝑥+𝑥=21 in ℝ.

  • A{4,096}
  • B{24}
  • C{144}
  • D{2,048}
  • E{64}

Q20:

Find the solution set of 1𝑥+1𝑥+1𝑥=3logloglog in ℝ.

  • A{8}
  • B{6}
  • C{2}
  • D{16}
  • E{4}

Q21:

Find the solution set of loglog𝑥−𝑥=2 in ℝ.

  • A{27}
  • B{18}
  • C{216}
  • D{6}
  • E{9}

Q22:

Find the solution set of 1𝑥+1𝑥=2loglog in ℝ.

  • A{8}
  • B{9}
  • C{6}
  • D{6,561}
  • E{18}

Q23:

Given that 𝐴𝐷 bisects ∠𝐴, find the value of 𝑥.

Q24:

Find the solution set of loglog5=3 in ℝ.

  • A{0}
  • B{5}
  • C{2}
  • D{1}
  • E{3}

Q25:

True or False: The solution set of loglog32−(𝑥−1)=53 in ℝ is {2}.

  • ATrue
  • BFalse

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