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Logarithmic Inequalities

Logarithmic Inequalities Warmup


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

log2(x2)+log2(x3)<1\log_{2}(x-2) + \log_{2}(x-3) < 1

What values of xx satisfy the above statement?

How many integer values of xx satisfy this inequality?

ln(2x)>ln(x23)\ln(2x) > \ln(x^2-3)

What values of xx satisfy the relationship

log6(x3)<log7(x3)\log_{6}(x-3) < \log_{7}(x-3)

log5(x5)<2\log_{5}(x-5) < 2

Solve for x.


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