## Exercises for Using and DerivingAlgebraic Properties of Logarithms miscellaneous on-line topics for Calculus Applied to the Real World

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1. Let $a = \ln 2,$ $b = \ln 3$ and $c = \ln 5.$ Use the identities for logarithms to express the following quantities in terms of $a,$ $b$ and $c.$
 (a) $\ln 6 =$ (b) $\ln (1/5) =$ (c) $\ln (2/3) =$ (d) $\ln 256 =$ (e) $\ln 0.3 =$ (f) $\ln 0.02 =$ (g) $\ln (9/e) =$

2. Complete the following equations by filling in the missing quantity.

 (a) $\log_a3 + \log_a4 = \log_a$ (b) $\log_a3 - \log_a4 = \log_a$ (c) $2 \log_ax + \log_ay = \log_a$ (d) $2 \ln x + 4 \ln y - \ln z = \ln$ (e) $x\log 2 - \log(2x^2) = \log$

2. Solve the following equations for the indicated variable.

 (a) $4 = 2^x$ $x =$ (b) $9 = 3^{-x}$ $x =$ (c) $2^{-m} = 2^.2^m ^.4^m$ $m =$ (d) $100 = 50e^{3t}$ $t =$

Last Updated:October, 1999