Worksheet: Logarithmic Equations with Like Bases

In this worksheet, we will practice solving logarithmic equations with like bases using the laws of exponents and logarithms.

Q1:

Determine the solution set of the equation logloglog(𝑥6)+(𝑥+6)=64 in .

  • A{10}
  • B{2}
  • C{8}
  • D{2,2}
  • E{10,10}

Q2:

Find 𝑥 such that log(4𝑥4)=2.

  • A26
  • B26
  • C24
  • D24

Q3:

Solve the equation log𝑥𝑥2=1, where 𝑥.

  • A{1,2}
  • B{1,2}
  • C{3,4}
  • D{12,12}
  • E{3,4}

Q4:

Find the solution set of loglog(2𝑥+48)=2𝑥 in .

  • A{6}
  • B{14}
  • C{8}
  • D{5}
  • E{7}

Q5:

Solve log𝑥26𝑥7𝑥+6=1, where 𝑥.

  • A{1,4}
  • B{6,4}
  • C{6,4}
  • D{6}

Q6:

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

  • A27,7
  • B27,114
  • C{49,14}
  • D{14,14}
  • E72,14

Q7:

Determine the solution set of the equation loglog𝑥=4(𝑥+6) in .

  • A{10}
  • B{6}
  • C{2}
  • D{1}
  • E{8}

Q8:

What is the solution set of the equation log(9𝑥18)=2?

  • A
  • B{2}
  • C{3,6}
  • D209

Q9:

Find the solution set of logloglog9𝑥27=2𝑥+13216 in .

  • A{4}
  • B{9}
  • C338
  • D{6}
  • E{3}

Q10:

Find the solution set of loglogloglog5+4024=2+8 in .

  • A54
  • B{2}
  • C14
  • D45

Q11:

Determine the solution set of the equation 2×5=64,000loglog in .

  • A{3}
  • B{8}
  • C{27}
  • D{40}

Q12:

Find the solution set of loglog𝑥2×2𝑥=4 in .

  • A{20,10}
  • B100,1100
  • C20,150
  • D200,150
  • E{200,100}

Q13:

Find the solution set of loglogloglog216×81=36×𝑥 in .

  • A{2}
  • B{9}
  • C{81}
  • D{27}
  • E{3}

Q14:

Solve 5=15log, where 𝑥.

  • A6
  • B1
  • C16
  • D65

Q15:

Solve log(2+510)=10𝑥, where 𝑥.

Q16:

Determine the solution set of the equation loglog𝑥5𝑥+4=4+(𝑥1) in .

  • A{85}
  • B{77}
  • C{4}
  • D{1}

Q17:

Solve the equation log𝑥=5𝑥, where 𝑥.

  • A30
  • B7
  • C10
  • D17
  • E175

Q18:

If 8𝑥+5𝑦𝑥𝑦=3logloglog, what is the value of 𝑥𝑦?

  • A406
  • B6
  • C66
  • D36

Q19:

Determine the solution set of 503+3=8loglog in .

  • A{4}
  • B{6}
  • C{12}
  • D{9}

Q20:

Find the value of 𝑥 for which log2433=112.

Q21:

Find the solution set of loglog17+𝑥+5=𝑥121 in .

  • A{2}
  • B{27}
  • C{5}
  • D{343}
  • E{15}

Q22:

Find the solution set of loglog64𝑥=4 in .

  • A{7}
  • B{256}
  • C{4}
  • D{1}

Q23:

Given that 10𝑥+12𝑦𝑥𝑦=7(7+10)logloglogloglog, determine the value of 𝑥.

  • A70𝑦
  • B8𝑦
  • C7𝑦
  • D49𝑦
  • E17𝑦

Q24:

Find the solution set of 𝑥=10log in .

  • A{64}
  • B{8,8}
  • C10,10
  • D{3,3}
  • E{1,000,0.001}

Q25:

Find the value of 𝑥 for which log243=5.

  • A15
  • B13
  • C53
  • D8
  • E35

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