Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$\log x ^ { 3 } = ( \log x ) ^ { 3 }$$
A) {1, 3}
B) {1, 0.138}
C) {0, 1}
D) {1, 0.019, 53.957}

Question

Quizplus · Accepted Answer

To solve the equation $\log x^3 = (\log x)^3$ graphically, we plot two functions: $y = \log x^3$ and $y = (\log x)^3$, and find their points of intersection. Simplifying the left side gives $y = 3\log x$, because of the logarithmic property $\log a^b = b\log a$. The points of intersection give the solutions to the equation. Graphically, the solutions are approximately $x = 1$, $x \approx 0.019$, and $x \approx 53.957$, which corresponds to choice D.

Solve the Following Graphically log⁡x3=(log⁡x)3\log x ^ { 3 } = ( \log x ) ^ { 3 }logx3=(logx)3

Solve the Following Graphically $\log x ^ { 3 } = ( \log x ) ^ { 3 }$