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CHAPTER 13 REVIEW EXERCISES

Concept check Exercises

Determine each of the following as being either true or false. If it is false, explain why.

$y = - 6^{- x}$ is an exponential function.
The logarithmic form of $y = - 2^{- x}$ is $x = - \log_{- 2} y .$
$\log \frac{4}{5} = \frac{\log 4}{\log 5}$
$\log (\frac{1}{100}) = - 2$
$2 \ln x = \frac{\ln x^{2}}{- \ln e}$
If $2 \ln x - 1 = \ln x,$ then $x = e .$

Practice and Applications

In Exercises 7–18, determine the value of x.

$\log_{10} x = 4$
$\log_{9} x = 3$
$\log_{5} x = - 1$
$\log_{4} (sin x) = - 0.5$
$2 \log_{1/2} 8 = x$
$\log_{12} 144 = x - 3$
$\log_{8} 32 = x + 1$
$\log_{9} 27 = x$
$\log_{x} 36 = 2$
$\log_{x} (1/243) = 5$
$\log_{x} 10 = \frac{1}{3}$
$\log_{x} 8 = 0$

In Exercises 19–30, express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.

$\log_{3} 6 x$
$\log_{5} (\frac{7}{a^{3}})$
$\log_{3} (t^{2})$
$\log_{6} \sqrt{5}$
$\log_{2}$

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