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Solve the logarithmic equation $\log \left(x^2\right)-\log \left(x\right)=3$

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Final answer to the problem

The equation has no solutions.

Step-by-step Solution

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The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log \left(\frac{x^2}{x}\right)=3$

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$\log \left(\frac{x^2}{x}\right)=3$

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Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log(x^2)-log(x)=3. 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). Simplify the fraction \frac{x^2}{x} by x. Express the numbers in the equation as logarithms 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 to the problem

The equation has no solutions.

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Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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