Solving Log Equations (Log=number)

A logarithmic equation is an equation containing a variable in a logarithmic expression.

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Una ecuación logarítmica es una ecuación que contiene una variable en una expresión logarítmica

Solving with Logs on ONE Side of =

Resolviendo con Registros en UN Lado de =

• 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

​Condense los registros, si es posible (suma a multiplicación, resta a división)

Aísle el término logarítmico (sumar/restar, dividir por coeficiente)

Cambiar a Forma Exponencial

Resuelva la ecuación restante

​Another Example

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

$$\log_3v=4$$  

• 12

• 7

• 81

• 4

• 3

Multiple Choice

7log(9x-7)=0

*Hint: undo operations outside log FIRST!

• $$\frac{9}{8}$$  

• $$\frac{8}{9}$$  

• 0

• 1

• $$\frac{7}{9}$$  

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

log₃ (x-3) + 10 = 14

• 5

• 13

• 84

• -20

Multiple Choice

log₈(4x+4)=2

• 15

• 12

• 10

• 3

Multiple Choice

log₂(x + 5) = 3

• 3

• 4

• 5

• 6

Multiple Choice

Solve for x. $$\log_8\left(x+4\right)=2$$  

• 12

• 60

• 64

• No solution

Multiple Choice

7log(9x-7)=0

*Hint: undo operations outside log FIRST!

• $$\frac{9}{8}$$  

• $$\frac{8}{9}$$  

• 0

• 1

• $$\frac{7}{9}$$