ln(20) + ln(5) = 2 ln(<em>x</em>)
ln(20×5) = ln(<em>x</em> ²)
ln(100) = ln(<em>x</em> ²)
100 = <em>x</em> ²
<em>x</em> = 10
The length of the hypotenuse in inches is 2 square root 13
1 ) log ( 16 ) 4 = 1/2
Answer: B ) 1/2
2 ) 125 ^( 9 x - 2 ) = 150
9 x - 2 = log ( 125 ) 150
9 x - 2 = 1.038
9 x = 1.038 + 2
9 x = 3.038
x = 3.038 : 9
x = 0.3375
Answer: C ) 0.3375
3 ) log ( 3 x + 2 ) = 3
3 x + 2 = 10^3
3 x + 2 = 1000
3 x = 1000 - 2
3 x = 998
x = 998 / 3
Answer: B ) 998 / 3
<span>(a) Triangles ABC and PQR are similar triangles since they both share 2 congruent angles and therefore their 3rd angle is also congruent. So the triangles are similar due to the AAA similarity theorem.
(b) The area of triangle PQR is 1 million times larger than the area of triangle ABC. This can be shown since the area of a triangle is 1/2 base times height. You can show that the base of triangle PQR is 1000 times larger than the base of triangle ABC. And since all the sides are in proportion to each other, the height of triangle PQR is also 1000 times larger than the height of triangle ABC. And since 1000 times 1000 equals 1,000,000 or 1 million, the area of triangle PQR is 1 million times larger than triangle ABC.</span>
