Logarithmic and Exponential Equations

Check if the equation can be simplified.

Isolate the variable on one side.

Check if common bases can be found.

Convert the equation to a quadratic form.

Multiply both sides by the base of the logarithm.

Add a constant to both sides.

Change the logarithm into its exponential form.

Convert the logarithm into a polynomial.

Exponential

Subtraction

Addition

Multiplication

Subtract 3 from both sides.

Divide both sides by 2.

Convert the logarithm to exponential form.

Add 1 to both sides.

If the constant is positive.

If the logarithm is isolated.

If the constant is a multiple of the base.

If the logarithm can be simplified.

2

1

e

10

Multiply both sides by the base.

Add a constant to both sides.

Isolate the exponential expression.

Convert the equation to a logarithmic form.

Add 7 to both sides.

Subtract 5 from both sides.

Multiply both sides by e.

Divide both sides by 5.

To isolate the variable.

To separate the base and exponent.

To simplify the equation.

To find common bases.

Divide both sides by 5.

Subtract 4 from both sides.

Use common bases to simplify.

Convert the logarithm to exponential form.