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Worksheet: Writing a Logarithmic Equation in Exponential Form

Q1:

Express l o g 3 4 3 7 = 1 3 in its equivalent exponential form.

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

Q2:

Express l o g 6 1 3 6 = 2 in its equivalent exponential form.

  • A 6 1 3 6 = 2
  • B ( 2 ) = 1 3 6 6
  • C l o g 1 3 6 = 1 2
  • D 6 = 1 3 6 2
  • E ( 2 ) = 3 6 1 0

Q3:

Solve for .

  • A
  • B
  • C
  • D
  • E

Q4:

The intensity levels 𝐼 of two earthquakes measured on a seismograph can be compared by the formula where 𝑀 is the magnitude given by the Richter Scale. In August 2009, an earthquake of magnitude 6.1 hit Honshu, Japan. In March 2011, that same region experienced another earthquake with a magnitude of 9.0. How many times greater was the intensity of the 2011 earthquake? Round to the nearest whole number.

Q5:

Solve for 𝑥 𝑥 = 2 l o g 5 .

  • A 𝑥 = 1 0
  • B 𝑥 = 5
  • C 𝑥 = 3 2
  • D 𝑥 = 2 5
  • E 𝑥 = 2

Q6:

Consider the logarithmic equation l o g 5 2 5 = 𝑥 .

Convert the equation to exponential form.

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

Solve the equation.

  • AThere is no solution
  • B 𝑥 = 0 . 5
  • C 𝑥 = 1 . 9 0 4
  • D 𝑥 = 2