Solve the inequality: $\frac { 1 } { 3 } \leq \log x

Question

Solve the inequality: $\frac { 1 } { 3 } \leq \log x < 1$
A) $- 30 \leq x < 10$

B) $\sqrt { 10 } + 1 / 3 \leq x < 10$

C) $- 10 \leq x < 10$

D) $\sqrt [ 3 ] { 10 } \leq x < 10 ^ { 3 }$

E) $\sqrt [ 3 ] { 10 } \leq x < 10$

Quizplus · Accepted Answer

The inequality $\frac { 1 } { 3 } \leq \log x < 1$ can be solved by converting the logarithmic inequality into its exponential form. The base of the logarithm is 10 by default. So, the inequality translates to $10^{\frac{1}{3}} \leq x < 10^1$, which simplifies to $\sqrt[3]{10} \leq x < 10$.

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Solve the Inequality $\frac { 1 } { 3 } \leq \log x < 1$