Logarithms Problem set A Answers

1. (a) \(x = \frac{1}{1000}\)
2. (b) \(y = \frac{401}{100}\)
3. (c) \(t = \frac{9}{2}\)

1. (a) \(x = e^3 = 20.1\)
2. (b) \(x = e^{-2.5} = 0.0821\)
3. (c) \(x = \frac{e^2+3}{4} = 2.60\)

1. (a) \(5 p - 2 q\)
2. (b) \(\frac{2 p}{3} + \frac{q}{3}\)
3. (c) \(\frac{p}{2} - 3 q + 3\)

1. (a) \(x = \frac{25}{2}\)
2. (b) \(x = 16\)

1. (a) \(x = 4\)
2. (b) \(x = \frac{e^3+1}{e^3-2} = 1.17\)

1. (a) \(x = \frac{2\ln 3 + \ln 4}{\ln 4 - \ln 3} = 12.5\)
2. (b) \(x = \frac{\ln 2}{\ln 7 - 3\ln 2} = -5.19\)

1. (a) \(x = −1.40\)
2. (b) \(x = 33\)
3. (c) \(x = 6.31\)

1. (a) \(x = 3.40\)
2. (b) \(x = e^3 = 20.1\)
3. (c) \(x = 33.1\)

1. (a) \(\text{pH} = 4.52\)
2. (b) \(h = 6.31 \times 10^{-5}\)

1. (a) \(H = 5.45\) m
2. (b) \(t = e^2 = 7.39\) years

\(t = \frac{\ln 1.5}{\ln(1.03/0.99)} = 10.2\) years

1. (a) \(M = 5.30\)
2. (b) \(A = 31 600\) micrometres

1. (a) \(C = 53.0\%\)
2. (b) \(t = e^2 = 7.39\) hours

1. (a) b = 1.32, a = 2.55
2. (b) D = 7.71 cm
3. (c) t = 62.4 years

1. (a) \(E=6.31\times10^{13}\) J
2. (b) M = 7.00
3. (c) 1000 times

\(x = 5\)

\(x = \frac{\ln 15}{\ln 1.8} = 4.61\)