Lesson Worksheet: Logarithmic Equations with Different Bases Mathematics • 10th Grade

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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:

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

  • A{27}
  • B127
  • C3√3
  • D13√3

Q3:

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

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

Q4:

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

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

Q5:

Find the solution set of loglog𝑥−𝑥=6 in ℝ.

  • A{6}
  • B{3}
  • C{9}
  • D{2}
  • E{8}

Q6:

Solve loglog𝑥−8𝑥=1, where 𝑥∈ℝ.

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

Q7:

Solve logloglog36=0, where 𝑥∈ℝ.

Q8:

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

  • A{2}
  • B{64}
  • C{32}
  • D{6}

Q9:

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

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

Q10:

Solve loglog251+(𝑥+7)=8, where 𝑥∈ℝ.

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