Worksheet: Converting between Logarithmic and Exponential Forms

In this worksheet, we will practice converting between logarithmic and exponential forms of equations.

Q1:

Express 4=1 in logarithmic form.

  • Alog4=1
  • Blog0=1
  • Clog1=0
  • Dlog4=0

Q2:

Express 97=8149 in its equivalent logarithmic form.

  • Alog8149=97
  • Blog97=2
  • Clog8149=187
  • Dlog8149=2

Q3:

Express 3438=72 in its equivalent logarithmic form.

  • Alog72=1,0298
  • Blog72=3438
  • Clog3438=13
  • Dlog72=13

Q4:

Express 243=3 in its equivalent logarithmic form.

  • Alog3=15
  • Blog15=243
  • Clog3=243
  • Dlog3=2435
  • E3=15

Q5:

Express 4=116 in its equivalent logarithmic form.

  • A116=4
  • Blog116=4
  • Clog4=2
  • Dlog116=8
  • Elog116=2

Q6:

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

  • A0.343=3
  • Blog0.343=3
  • Clog0.343=0.7
  • Dlog0.7=3
  • Elog0.343=2.1

Q7:

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

  • Alog0.4=12
  • Blog0.4=0.16
  • Clog0.16=12
  • Dlog0.16=0.8
  • E0.16=12

Q8:

Express 2=42 in its equivalent logarithmic form.

  • Alog42=52
  • Blog42=2
  • Clog42=52
  • Dlog2=52
  • Elog42=5

Q9:

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

  • Alog1,000=3
  • Blog3=1,000
  • C1,000=10
  • Dlog1,000=10
  • Elog1,000=30

Q10:

Express 2=1162 in its equivalent logarithmic form.

  • Alog1162=92
  • Blog1162=9
  • Clog1162=2
  • Dlog1162=2
  • Elog2=92

Q11:

Express 2=512 in its equivalent logarithmic form.

  • Alog512=182
  • Blog512=2
  • Clog512=18
  • Dlog2=18

Q12:

Express 8=𝑦 in its equivalent logarithmic form.

  • Alog8=𝑥
  • Blog𝑦=8𝑥
  • Clog𝑦=𝑥
  • Dlog𝑦=8

Q13:

Express log1273=72 in its equivalent exponential form.

  • A3=1273
  • B1273=3
  • Clog1273=212
  • D72=1273
  • E1273=3

Q14:

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

  • A6=1,000,000
  • B10=1,000,000
  • Clog1,000,000=60
  • D1,000,000=10

Q15:

Express log4=2 in its equivalent exponential form.

  • A4=2
  • B2=4
  • C2=4
  • Dlog4=4

Q16:

Express log27343=3 in its equivalent exponential form.

  • A27343=37
  • Blog27343=97
  • C27343=3
  • D27343=3
  • E37=27343

Q17:

Express log2433=112 in its equivalent exponential form.

  • A2433=3
  • B3=2433
  • C112=2433
  • Dlog2433=332

Q18:

Write the exponential equation 𝑒=5 in logarithmic form.

  • A𝑥=5ln
  • B𝑥=15ln
  • C𝑥=15
  • D𝑥=5

Q19:

Write the logarithmic equation 8=𝑥ln in exponential form.

  • A𝑒=𝑥
  • B𝑒=𝑥
  • C𝑒8=𝑥
  • D8𝑒=𝑥

Q20:

Express log7=13 in its equivalent exponential form.

  • A7=13
  • B343=3
  • Clog7=3433
  • D343=7
  • E13=343

Q21:

Express log136=2 in its equivalent exponential form.

  • A(2)=36
  • Blog136=12
  • C136=2
  • D(2)=136
  • E6=136

Q22:

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

  • A𝑥=66
  • B66=66
  • C66=𝑦
  • D𝑦=66
  • E𝑥=𝑦

Q23:

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

  • A𝑎=𝑐
  • B𝑐=𝑏
  • C𝑐=𝑎
  • D𝑎=𝑏
  • E𝑏=𝑐

Q24:

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

  • A𝑥=𝑧
  • B2=𝑥
  • C𝑧=𝑥
  • D𝑧=2
  • E𝑥=2

Q25:

Express log(𝑧)=12 in its equivalent exponential form.

  • A20=𝑧
  • B𝑧=20
  • C𝑧=12
  • D12=20
  • E12=𝑧

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