Step-by-step Solution

Solve the logarithmic equation $\log \left(x+1\right)=\log \left(x-1\right)+3$

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Step-by-step solution

Problem to solve:

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

Learn how to solve logarithmic equations problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log(10,x+1)=log(10,x-1)+3. Grouping terms. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). 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.

Final Answer

$x=1.002002$
$log\left(x+1\right)=log\left(x-1\right)+3$

Main topic:

Logarithmic Equations

Time to solve it:

~ 0.09 s