Solve the logarithmic equation $\log \left(x\right)-\log \left(2\right)=\log \left(x+8\right)-\log \left(x+2\right)$

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Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log(x)-log(2)=log(x+8)-log(x+2). 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). 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). 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. Apply fraction cross-multiplication.