Solving Logarithmic Equations Concepts

To change the base of the logarithm

To add more logarithms

To remove the logarithm

To evaluate the logarithm

Add 7 to both sides

Multiply both sides by 3

Subtract 7 from both sides

Divide both sides by 3

ln(x^2) = -3

ln(x) = 2

ln(x^3) = -2

ln(x) = -2

Exponentiation and division

Exponentiation and rewriting in logarithmic form

Multiplication and division

Addition and subtraction

Base 5

Base 10

Base 2

Base e

x = e^2

x = e^(-2/3)

x = e^3

x = e^(-1/2)

The equation becomes more complex

The logarithm cancels out

The exponent doubles

The base changes to 10

It has no effect

It complicates the equation

It changes the base

It simplifies the equation

x = e^(2/3)

x = e^(-2/3)

x = e^(1/3)

x = e^(-1/3)

There is only one correct method

Multiple methods can lead to the same solution

The base of the logarithm must always be changed

The logarithm must always be evaluated