Solved example of logarithmic equations
Grouping terms
The difference of two logarithms of same base is equal to the logarithm of the division
Simplify $\frac{-1}{1}$ multiplying the denominator by $-1$
Rewrite the number $3$ as a logarithm of base $10$
For two logarithms of the same base to be equal, their arguments must be equal. In other words, if $\log(a)=\log(b)$ then $a$ must equal $b$
$-1$ is not equal to $1000$
Verify that the solutions obtained are valid in the initial equation
The valid solutions to the logarithmic equation are the ones that, when replaced in the original equation, don't result in any logarithm of negative numbers or zero, since in those cases the logarithm does not exist
Access detailed step by step solutions to thousands of problems, growing every day!