Solve the problems. a.5=2.25^x b. 3.5^x=10 c.2(8^x)=128 d.2x^8=128

Answer 1

5 = 2.25^x

ln 5 = ln 2.25 x

1.609 ≈ 0.811 x

1.984 ≈ x

Use this as a model to solve the others.

Answer 2

a) 5 = 2.25^x, x= about 2. 2.25^2 = 5.0625. so x is slightly less than 2

b) x= about 1.838. 3.5^1.838 = very close to 10

c) x=2. 2(8^x)= 128, 8^x = 128/2 = 64, 8^2 = 64

d) 2x^8 = 128

x^8 = 128/2 = 64

x^4 = sqr64 = 8

x^2 = sqr8 = 2sqr2

x= 4th root of 8 = sqr2 times the 4th root of 2 = about 1.68

2(1.68)^8 = 126.9 = close to 128

x= slightly more than 1.68