Solve the following for xlog(2x)-log(x-3)=1

Isolate Logarithmic Terms: Isolate the logarithmic terms on one side of the equation. We want to group the logarithmic terms together to apply logarithmic properties. We can do this by adding log(x - 3) to both sides of the equation. xlog(2x) - log(x - 3) + log(x - 3) = 1 + log(x - 3) This simplifies to: xlog(2x) = 1 + log(x - 3)Combine Logarithmic Terms: Apply the property of logarithms to combine the terms on the right side of the equation. We can use the property of logarithms that states log(a) + log(b) = log(ab) to combine the 1 and log(x - 3) on the right side of the equation. However, we cannot directly apply this property because 1 is not a logarithm. This is a math error.

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Solve the following for `x` $\newline$ $\log(2x)-\log(x-3)=1$

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Precalculus

Product property of logarithms

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Q. Solve the following for `x`

\newline

\log(2x)-\log(x-3)=1

Isolate Logarithmic Terms: Isolate the logarithmic terms on one side of the equation. $\newline$ We want to group the logarithmic terms together to apply logarithmic properties. We can do this by adding $\log(x - 3)$ to both sides of the equation. $\newline$ $x\log(2x) - \log(x - 3) + \log(x - 3) = 1 + \log(x - 3)$ $\newline$ This simplifies to: $\newline$ $x\log(2x) = 1 + \log(x - 3)$
Combine Logarithmic Terms: Apply the property of logarithms to combine the terms on the right side of the equation. $\newline$ We can use the property of logarithms that states $\log(a) + \log(b) = \log(ab)$ to combine the $1$ and $\log(x - 3)$ on the right side of the equation. However, we cannot directly apply this property because $1$ is not a logarithm. This is a math error.