Solve the equation.
-$( \log x ) ^ { 2 } = \log x ^ { 2 }$
A) { }
B) $\{ 1,100 \}$
C) $\{ 1 \}$
D) $\{ 100 \}$

Question

Solve the equation.
-$( \log x ) ^ { 2 } = \log x ^ { 2 }$
A) {  }
B) $\{ 1,100 \}$
C) $\{ 1 \}$
D) $\{ 100 \}$

Quizplus · Accepted Answer

The equation $(\log x)^2 = \log x^2$ can be solved by recognizing that $\log x^2 = 2\log x$. Setting $(\log x)^2 = 2\log x$, we can rewrite this as $(\log x)^2 - 2\log x = 0$, which factors to $\log x(\log x - 2) = 0$. This gives us two solutions: $\log x = 0$ and $\log x = 2$. Solving these, we find $x = 10^0 = 1$ and $x = 10^2 = 100$, respectively. Therefore, the solution set is $\{1, 100\}$.

Solve the Equation (log⁡x)2=log⁡x2( \log x ) ^ { 2 } = \log x ^ { 2 }(logx)2=logx2

Solve the Equation $( \log x ) ^ { 2 } = \log x ^ { 2 }$