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How to Solve Logarithmic Inequalities

When you solve logarithmic inequalities, you use the same rules for equations as you are used to.

Rule

Logarithmic inequalities

aking the exponent on both sides of an inequality does not change the inequality. Thus, nothing happens to the inequality sign! log x < c ln x < c 10log x < 10c eln x < ec x < 10c x < ec

Example 1

Solve the inequality ln (x 4) 8 ln (x 4) 8 eln (x4) e8 x 4 e8 x e8 + 4 x 2984.96

Example 2

Solve the inequality log (2x + 3) 4

log (2x + 3) 4 eln (2x+3) e4 2x + 3 e4 2x e4 3 | ÷ (2) x e4 3 2 = 3 e4 2 You need to flip the inequality sign when you divide by a negative number. You must have an equality sign in the last row as the answer is just changed to look nicer.

Example 3

Solve the inequality ln (x 3) e ln (x 3) e eln (x3) ee x 3 ee x ee + 3 18.15

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How to Solve Exponential Inequalities