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Logarithmic equations Calculator

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1

Solved example of logarithmic equations

$log\left(x+1\right)=log\left(x-1\right)+3$
2

Grouping terms

$\log \left(x+1\right)-\log \left(x-1\right)=3$
3

The difference of two logarithms of same base is equal to the logarithm of the division

$\log \left(\frac{x+1}{x-1}\right)=3$
4

Simplify $\frac{-1}{1}$ multiplying the denominator by $-1$

$\log \left(-1\right)=3$
5

Rewrite the number $3$ as a logarithm of base $10$

$\log \left(-1\right)=\log \left(1000\right)$
6

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 $b$

$-1=1000$
7

$-1$ is not equal to $1000$

false

Verify that the solutions obtained are valid in the initial equation

8

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

No solution.

Final Answer

No solution.

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