Exercise 29 Page 496

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

{ n | n > 0.6667 }

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. 6^(3n) > 36 ⇔ log 6^(3n) > log 36 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 6^(3n) > log 36

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

3n log 6 > log 36

WritePow

Write as a power

3n log 6 > log 6^2

log(a^m)= m*log(a)

3n log 6 >2 log 6

DivEqn

.LHS /log 6.=.RHS /log 6.

3n >2

DivEqn

.LHS /3.=.RHS /3.

n > 2/3

UseCalc

Use a calculator

n > 0.6667

Finally, we can write our answer in set-builder notation. { n | n > 0.6667 }

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 29 Page 496

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