Mixed exponent and logarithm practice Problem set A Answers

1. (a) \(3x+y\)
2. (b) \(2y-x-4z\)
3. (c) \(3+\tfrac12y-2x\)

1. (a) \(\ln(a^4b^2)\)
2. (b) \(\ln\dfrac{\sqrt x}{y^3}\)
3. (c) \(\ln27\)

1. (a) x = 95
2. (b) x = 4
3. (c) x = 8.39

1. (a) x = 1.75
2. (b) x = 1.70
3. (c) x = 41.0

1. (a) \(-\tfrac32\)
2. (b) \(\tfrac23\)
3. (c) \(\tfrac52\)

1. (a) x = 3
2. (b) \(x=\tfrac17\)
3. (c) x = 4

1. (a) x = −12
2. (b) x = 9
3. (c) \(x=-\tfrac32\)

x = ln 50 / ln 1.6 = 8.32

1. (a) x = 25
2. (b) x = 7.1
3. (c) x = 4.73

1. (a) x = 5
2. (b) \(x = \frac{3}{2}\)
3. (c) x = 13

1. (a) 80 mg
2. (b) 49.1 mg
3. (c) t = 8.53 hours

t = 6.34 days

8.47 years

1. (a) 250; 2620
2. (b) t = 7.85 hours
3. (c) 60%

1. (a) 5730 years
2. (b) 9950 years

1. (a) k = 0.0875
2. (b) t = 16.3 years

1. (a) \(2^x=\tfrac{15}2\)
2. (b) x = 2.91

1. (a) \(x=1000,\ y=10\)
2. (b) \(x=100,\ y=e^3\approx20.1\)

1. (a) \(-a^{b/2}\)
2. (b) \(a^{5}\)

x = 3