Worksheet: Converting between Logarithmic and Exponential Forms

In this worksheet, we will practice utilizing the relationship between logarithms and exponentials to convert an exponential expression to its logarithmic form.

Q1:

Express 4=1 in logarithmic form.

  • A l o g 4 = 1
  • B l o g 0 = 1
  • C l o g 1 = 0
  • D l o g 4 = 0

Q2:

Express 97=8149 in its equivalent logarithmic form.

  • A l o g 8 1 4 9 = 9 7
  • B l o g 9 7 = 2
  • C l o g 8 1 4 9 = 1 8 7
  • D l o g 8 1 4 9 = 2

Q3:

Express 3438=72 in its equivalent logarithmic form.

  • A l o g 7 2 = 1 , 0 2 9 8
  • B l o g 7 2 = 3 4 3 8
  • C l o g 3 4 3 8 = 1 3
  • D l o g 7 2 = 1 3

Q4:

Express 243=3 in its equivalent logarithmic form.

  • A l o g 3 = 1 5
  • B l o g 1 5 = 2 4 3
  • C l o g 3 = 2 4 3
  • D l o g 3 = 2 4 3 5
  • E 3 = 1 5

Q5:

Express 4=116 in its equivalent logarithmic form.

  • A 1 1 6 = 4
  • B l o g 1 1 6 = 4
  • C l o g 4 = 2
  • D l o g 1 1 6 = 8
  • E l o g 1 1 6 = 2

Q6:

Express (0.7)=0.343 in its equivalent logarithmic form.

  • A 0 . 3 4 3 = 3
  • B l o g 0 . 3 4 3 = 3
  • C l o g 0 . 3 4 3 = 0 . 7
  • D l o g 0 . 7 = 3
  • E l o g 0 . 3 4 3 = 2 . 1

Q7:

Express (0.16)=0.4 in its equivalent logarithmic form.

  • A l o g 0 . 4 = 1 2
  • B l o g 0 . 4 = 0 . 1 6
  • C l o g 0 . 1 6 = 1 2
  • D l o g 0 . 1 6 = 0 . 8
  • E 0 . 1 6 = 1 2

Q8:

Express 2=42 in its equivalent logarithmic form.

  • A l o g 4 2 = 5 2
  • B l o g 4 2 = 2
  • C l o g 4 2 = 5 2
  • D l o g 2 = 5 2
  • E l o g 4 2 = 5

Q9:

Express 10=1,000 in its equivalent logarithmic form.

  • A l o g 1 , 0 0 0 = 3
  • B l o g 3 = 1 , 0 0 0
  • C 1 , 0 0 0 = 1 0
  • D l o g 1 , 0 0 0 = 1 0
  • E l o g 1 , 0 0 0 = 3 0

Q10:

Express 2=1162 in its equivalent logarithmic form.

  • A l o g 1 1 6 2 = 9 2
  • B l o g 1 1 6 2 = 9
  • C l o g 1 1 6 2 = 2
  • D l o g 1 1 6 2 = 2
  • E l o g 2 = 9 2

Q11:

Express 2=512 in its equivalent logarithmic form.

  • A l o g 5 1 2 = 1 8 2
  • B l o g 5 1 2 = 2
  • C l o g 5 1 2 = 1 8
  • D l o g 2 = 1 8

Q12:

Express 8=𝑦 in its equivalent logarithmic form.

  • A l o g 8 = 𝑥
  • B l o g 𝑦 = 8 𝑥
  • C l o g 𝑦 = 𝑥
  • D l o g 𝑦 = 8

Q13:

Express log1273=72 in its equivalent exponential form.

  • A 3 = 1 2 7 3
  • B 1 2 7 3 = 3
  • C l o g 1 2 7 3 = 2 1 2
  • D 7 2 = 1 2 7 3
  • E 1 2 7 3 = 3

Q14:

Express log1,000,000=6 in its equivalent exponential form.

  • A 6 = 1 , 0 0 0 , 0 0 0
  • B 1 0 = 1 , 0 0 0 , 0 0 0
  • C l o g 1 , 0 0 0 , 0 0 0 = 6 0
  • D 1 , 0 0 0 , 0 0 0 = 1 0

Q15:

Express log4=2 in its equivalent exponential form.

  • A 4 = 2
  • B 2 = 4
  • C 2 = 4
  • D l o g 4 = 4

Q16:

Express log27343=3 in its equivalent exponential form.

  • A 2 7 3 4 3 = 3 7
  • B l o g 2 7 3 4 3 = 9 7
  • C 2 7 3 4 3 = 3
  • D 2 7 3 4 3 = 3
  • E 3 7 = 2 7 3 4 3

Q17:

Express log2433=112 in its equivalent exponential form.

  • A 2 4 3 3 = 3
  • B 3 = 2 4 3 3
  • C 1 1 2 = 2 4 3 3
  • D l o g 2 4 3 3 = 3 3 2

Q18:

Write the exponential equation 𝑒=5 in logarithmic form.

  • A 𝑥 = 5 l n
  • B 𝑥 = 1 5 l n
  • C 𝑥 = 1 5
  • D 𝑥 = 5

Q19:

Write the logarithmic equation 8=𝑥ln in exponential form.

  • A 𝑒 = 𝑥
  • B 𝑒 = 𝑥
  • C 𝑒 8 = 𝑥
  • D 8 𝑒 = 𝑥

Q20:

Express log7=13 in its equivalent exponential form.

  • A 7 = 1 3
  • B 3 4 3 = 3
  • C l o g 7 = 3 4 3 3
  • D 3 4 3 = 7
  • E 1 3 = 3 4 3

Q21:

Express log136=2 in its equivalent exponential form.

  • A ( 2 ) = 3 6
  • B l o g 1 3 6 = 1 2
  • C 1 3 6 = 2
  • D ( 2 ) = 1 3 6
  • E 6 = 1 3 6

Q22:

Consider the logarithmic equation log25=𝑥.

Convert the equation to exponential form.

  • A 5 = 2 5
  • B 5 = 2 5
  • C 𝑥 = 2 5
  • D 2 5 = 5

Solve the equation.

  • A 𝑥 = 1 . 9 0 4
  • BThere is no solution
  • C 𝑥 = 2
  • D 𝑥 = 0 . 5

Q23:

Express 𝑦=(66)log in its equivalent exponential form.

  • A 𝑥 = 6 6
  • B 6 6 = 6 6
  • C 6 6 = 𝑦
  • D 𝑦 = 6 6
  • E 𝑥 = 𝑦

Q24:

Express log(𝑏)=𝑐 in its equivalent exponential form.

  • A 𝑎 = 𝑐
  • B 𝑐 = 𝑏
  • C 𝑐 = 𝑎
  • D 𝑎 = 𝑏
  • E 𝑏 = 𝑐

Q25:

Express 𝑧=(𝑥)log in its equivalent exponential form.

  • A 𝑥 = 𝑧
  • B 2 = 𝑥
  • C 𝑧 = 𝑥
  • D 𝑧 = 2
  • E 𝑥 = 2

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