# Worksheet: Logarithmic Equations with Different Bases

In this worksheet, we will practice solving logarithmic equations involving logarithms with different bases.

Q1:

Find the solution set of in .

• A
• B
• C
• D

Q2:

Find the solution set of in .

• A
• B
• C
• D

Q3:

Determine the solution set of the equation in .

• A
• B
• C
• D
• E

Q4:

Solve , where .

• A2
• B
• C
• D
• E4

Q5:

Find the solution set of in .

• A
• B
• C
• D
• E

Q6:

Determine the solution set of the equation in .

• A
• B
• C
• D

Q7:

Find the solution set of in .

• A
• B
• C
• D
• E

Q8:

Find the solution set of in .

• A
• B
• C
• D

Q9:

Find the solution set of in .

• A
• B
• C
• D
• E

Q10:

Find the solution set of in .

• A
• B
• C
• D

Q11:

Find the solution set of in .

• A
• B
• C
• D
• E

Q12:

Solve , where .

• A81
• B27
• C729
• D
• E

Q13:

Solve , where .

• A
• B
• C
• D
• E

Q14:

Solve , where .

Q15:

Solve , where .

• A
• B
• C
• D

Q16:

Solve , where .

• A or
• B or
• C or
• D or
• E or

Q17:

Solve , where .

Q18:

Find the solution set of in .

• A
• B
• C
• D

Q19:

The intensity levels of two earthquakes measured on a seismograph can be compared by the formula where 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.