Exercise 30 Page 496

Use the Inequality Property of Logarithmic Functions to rewrite the given exponential inequality as a logarithmic inequality.

{ x | x ≤ 1.0805 }

Practice makes perfect

To solve the given exponential inequality, we will use the Inequality Property of Logarithmic Functions.

Inequality Property of Logarithmic Functions
&Ifb > 1, log_b x > log_b y if and only if x > y. &Ifb > 1, log_b x < log_b y if and only if x < y.

Using this property, we can rewrite the exponential inequality as a logarithmic inequality. 2^(4x) ≤ 20 ⇔ log 2^(4x) ≤ log 20 To solve the above logarithmic inequality, we need to recall the Power Property of Logarithms.

Power Property of Logarithms
log_b m^p = p log_b m, where m and b are positive numbers, with b≠ 1.

Let's use it and solve the inequality!

log 2^(4x) ≤ log 20

log_()(a^m)= m* log_()(a)

4x log 2 ≤ log 20

DivEqn

.LHS /4 log 2.=.RHS /4 log 2.

x ≤ log 20/4 log 2

UseCalc

Use a calculator

x ≤ 1.0805

Finally, we can write our answer in set-builder notation. { x | x ≤ 1.0805 }

Subchapter links

Check Your Understanding p.495

Practice and Problem Solving p.495-497

H.O.T. Problems p.497

Standardized Test Practice p.498

Spiral Review p.498

Skills Review p.498

Exercise 30 Page 496

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