Logarithms Problem set B Answers

1. (a) \(x = \frac{1}{10000}\)
2. (b) \(y = \frac{6001}{1000}\)
3. (c) \(t = \frac{13}{4}\)

1. (a) \(x = e^{-2} = 0.135\)
2. (b) \(x = e^{-1.5} = 0.223\)
3. (c) \(x = \frac{e^3-2}{5} = 3.62\)

1. (a) \(4 p - 5 q\)
2. (b) \(\frac{p}{4} + \frac{3 q}{4}\)
3. (c) \(- 2 p + \frac{q}{3} + 4\)

1. (a) \(x = 250\)
2. (b) \(x = \frac{23}{2}\)

1. (a) \(x = \frac{28}{9}\)
2. (b) \(x = \frac{e^2+2}{e^2-3} = 2.14\)

1. (a) \(x = \frac{3\ln 2 + 2\ln 5}{\ln 5 - \ln 2} = 5.78\)
2. (b) \(x = \frac{\ln 3}{\ln 11 - 2\ln 3} = 5.47\)

1. (a) \(x = −0.155\)
2. (b) \(x = \frac{1005}{2}\)
3. (c) \(x = 5.62\)

1. (a) \(x = 2.48\)
2. (b) \(x = e^2 = 7.39\)
3. (c) \(x = 12.2\)

1. (a) \(L = 74.8\) decibels
2. (b) \(I = 3.16 \times 10^{-6}\) W/m²

1. (a) \(d = 7.89\) cm
2. (b) \(t = e^{2.24} = 9.39\) years

\(t = \frac{\ln 6.4}{\ln 1.5} = 4.58\) hours

1. (a) \(E = 5.40\)
2. (b) \(L = 39 800\) lux

1. (a) \(D = 34.3\) cm
2. (b) \(t = e^{2.5} = 12.2\) hours

1. (a) b = 8.93, a = 5.81
2. (b) P = 38.8%
3. (c) t = 36.7 years

1. (a) \(h=3.98\times10^{-4}\)
2. (b) pH = 3.60
3. (c) 1000 times

\(x = 2\)

\(x = \frac{\ln 14}{\ln(8/7)} = 19.8\)