Solving Logarithmic Equations Algebraically

Solving Logarithmic Equations

Solving With Logs of BOTH Sides of =

• Condense logs, if possible (Addition to Multiplication, Subtraction to Division)

• Logs cancel each other out

• Solve the remaining equation

Multiple Choice

Solve log₂(2x - 3) = log₂(4x + 5)

• 4

• -4

• -.33

• .33

Multiple Choice

Solve: $$\log_7\left(28+3r\right)=\log_7\left(10r\right)$$  

• 4

• 7

• 20

• 28

Multiple Choice

Solve: log₃ (5) + log₃(x) = log₃(2) + log₃(x + 9)

• 5

• 11

• 6

• 3

Solving with Logs on ONE Side of =

• Condense logs, if possible (Addition to Multiplication, Subtraction to Division)

• Isolate the log term (Add/Subtract, Divide by Coefficient)

• Change to Exponential Form

• Solve the Remaining Equation

Multiple Choice

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

Multiple Choice

log₃ (x-3) + 10 = 14

• 5

• 13

• 84

• -20

Multiple Choice

log₂(2) + log₂(8x) = 6

• x = 3
• x = 2
• x = 6
• x = 4

Solving Exponentials for Missing Exponents

• Isolate the exponential term (Add/Subtract, Divide by Coefficient)

• Change to logarithmic form

• Solve remaining equation (Change of Base Formula)

Multiple Choice

3^{2x – 6}  = 81

• x = log 4
• x = 5
• x = 4
• x = -1

Multiple Choice

7ⁿ⁺¹⁰- 8 = 6

• -7.374
• -8.643
• -7.360
• -8.853