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Logarithmic Inequalities

Logarithmic Inequalities - Base < 1

What is the range of $x$ that satisfies the logarithmic inequality $\log_{\frac{1}{3}}(5x-7) \geq \log_{\frac{1}{3}}(3x+5) ?$

\frac{5}{3} \leq x \leq 6

x \geq 6

\frac{7}{5} < x \leq 6

x \leq 6

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by Brilliant Staff

What is the maximum integer value of $x$ that satisfies the logarithmic inequality $\log_{\frac{1}{2}}(x-4) > \log_{\frac{1}{4}}(2x-5) ?$

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by Brilliant Staff

What is the range of $x$ that satisfies the logarithmic inequality $\log_{0.4}(x^2-23) - \log_{0.4}(x-5) < \log_{0.4}{7} ?$

x > 5

x < 3 \text{ or } x > 4

3 < x < 4

x < 3 \text{ or } x > 5

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by Brilliant Staff

What is the range of $x$ that satisfies the logarithmic inequality $\log_{0.5}{(2x+61)} > -3 ?$

-\frac{61}{2} < x < {53}

-{61} < x < -\frac{53}{2}

-\frac{61}{2} < x < -\frac{53}{2}

-\frac{53}{2} < x < \frac{61}{2}

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by Brilliant Staff

What is the range of $x$ that satisfies the logarithmic inequality $\log_{\frac{1}{5}}x > \log_{\frac{1}{7}}x ?$

0 < x < 1

6 < x < 8

1 < x < 2

5 < x < 7

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by Brilliant Staff

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