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Logarithmic Inequalities

Logarithmic inequalities are useful in analyzing situations involving repeated multiplication, such as interest and exponential decay.

Logarithmic Inequalities Warmup

True or false: $$\ln(10) > 2$$

$\log_{2}(x-2) + \log_{2}(x-3) < 1$

What values of $$x$$ satisfy the above statement?

How many integer values of $$x$$ satisfy this inequality?

$\ln(2x) > \ln(x^2-3)$

What values of $$x$$ satisfy the relationship

$$\log_{6}(x-3) < \log_{7}(x-3)$$

$\log_{5}(x-5) < 2$

Solve for x.

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