Since the enactment of a smoking ban in a particular​ city, the number of smokers has slowly declined. Statistics show that the number of smokers in this city has decreased for four consecutive months by​ 3%, 2%,​ 5%, and​ 2%. What was the overall percentage decrease in the number of smokers during this four month​ period? Round your answer to the nearest tenth of a percentage point.

ANSWER: x = -0.082

EXPLANATION:

1. Apply logarithm to both sides of the
equation. If one of the terms has base 10,
use common logarithm, otherwise, use
natural logarithm

2. Use the different properties of logarithms
to solve for the variable.

17
-92 _ 7 = 49
7.17-92 = 56
17-92 = 8
10g17(8)
-92
2
log, 7(8)
-9
log(8)
log(17)
-9
I=
-0.082
2 of 3
Add both sides by 7
Divide both sides by 7
Convert to logarithm
Divide both sides by - 9