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

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

Q1:

Given that log(𝑣+3)=1, find the value of 𝑣.

Q2:

Find 𝑥 such that log(4𝑥4)=2.

  • A26
  • B26
  • C24
  • D24

Q3:

What is the solution set of the equation log64=2?

  • A{6}
  • B{8}
  • C{12}
  • D{4}

Q4:

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}

Q5:

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

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

Q6:

Find the solution set of logloglog9𝑥26+𝑥+1=1282 in .

  • A{6}
  • B{3}
  • C{2}
  • D{10}
  • E{12}

Q7:

Find the solution set of 4(𝑥+5)(𝑥3)=625logloglog in .

  • A{7}
  • B{5}
  • C{11}
  • D{2}

Q8:

Find all possible values of 𝑥 for which 𝑥=64𝑥log.

  • A4 or 18
  • B12 or 118
  • C8 or 14
  • D8
  • E32

Q9:

Determine the number whose logarithm, with base 5, is 5.

  • A255
  • B25
  • C125
  • D125
  • E10

Q10:

Given that 𝐴𝐵𝐴𝐶 and 𝐴𝐷𝐵𝐶, determine the value of 𝑥. Give your answer to the nearest tenth.

This lesson includes 75 additional questions and 692 additional question variations for subscribers.

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