Mixed exponent and logarithm practice Problem set B Answers

1. (a) \(2x+3z\)
2. (b) \(3x-y-2z\)
3. (c) \(1+2z-\tfrac12x\)

1. (a) \(\ln(p^5q^3)\)
2. (b) \(\ln\dfrac{\sqrt[4]{m}}{n^2}\)
3. (c) \(\ln40\)

1. (a) x = 1007
2. (b) x = 24.75
3. (c) x = 2.48

1. (a) x = 2.12
2. (b) x = 2.67
3. (c) x = 61.4

1. (a) \(-\tfrac14\)
2. (b) \(\tfrac72\)
3. (c) \(\tfrac{11}3\)

1. (a) x = 5
2. (b) \(x=\tfrac14\)
3. (c) x = 9

1. (a) x = 3
2. (b) x = 8
3. (c) \(x=-\tfrac73\)

x = ln 405 / ln(25/3) = 2.83

1. (a) x = 12.5
2. (b) x = 3.01
3. (c) x = 1.10

1. (a) x = 4
2. (b) \(x = \frac{5}{2}\)
3. (c) \(x = \frac{11}{2}\)

1. (a) 24 000 euros
2. (b) 16 355.33 euros
3. (c) t = 6.85 years

t = 10.4 months

19.6 hours

1. (a) 320; 1940
2. (b) t = 9.16 weeks
3. (c) 35%

1. (a) 4.99 hours
2. (b) 13.6 hours

1. (a) k = 0.256
2. (b) t = 11.7 days

1. (a) \(2^x=\tfrac83\)
2. (b) x = 1.42

1. (a) \(x=10\,000,\ y=10\)
2. (b) \(x=1000,\ y=e^2\approx7.39\)

1. (a) \(-a^{b/3}\)
2. (b) \(a^{7}\)

x = 5