Logarithms: equations, systems and properties
1. Logarithm of a product 2. Logarithm of a quotient 3. Logarithm of a power 4. Change of base 5. Inverse
A logarithmic equation is an equation that has an unknown factor in the argument of a logarithm. In reality, the resolution is reduced to the resolution of equations of the same type as the expressions in the arguments (quadratic equations, cubic equations, irrational equations...).
Example 1 We will use the properties of logarithms and that We have an equality between logarithms, so the arguments (what is inside) has to be the same: The solution to the equation is x = 50.
3. Logrithmic equation systems
Example 1 We apply the change of variable This way we obtain the following linear equation system we resolve it and we undo the cange of variable:
Example 2 First we apply the property logarithm of a product: We apply the change of variable: and we obtain the following system: that has as solution: Finally, we undo the change of variable: We do not need to check the solutions.