5.04 Logarithms
Evaluate the following logarithmic expressions:
\log_{10} 1
\log_{10} 10
\log_{10} 100
\log_{10} 10\,000
\log_{10} 0.1
\log_{10} 0.001
3\log_{10} {100}
\dfrac{\log_{10} {0.01}}{\log_{10} {1000}}
Evaluate \log_{10} 45, to two decimal places.
Evaluate \log_{10} 5.16, correct to three decimal places.
Evaluate the following logarithmic expressions:
\log_{2} 8
\log_{4} 16
\log_{5} 1
\log_{5} 125
\log_{2} 16
\log_{3} 3
\log_{5} 0.2
\log_{4} 1
\log_{10} \left(\dfrac{1}{10}\right)
\log_{8} \left(\dfrac{1}{64}\right)
\log_{2} \left(\dfrac{1}{4}\right)
\log_{2} \left(\dfrac{1}{8}\right)
Evaluate the following logarithmic expressions:
\log_{0.2} 25
\log_{\frac{1}{10}} 10\,000
\log_{2} 0.25
\log_{0.9} 0.81
Evaluate the following logarithmic expressions:
\log_{36} 6
\log_{25} 5
\log_{8} 2
\log_{27} 3
\log_{10} {\sqrt{10}}
\log_{10} \dfrac{1}{\sqrt{10}}
\log_{3}{\sqrt{3}}
\log_{5}{\left(\sqrt[3]{5}\right)}
Rewrite each of the following equations in logarithmic form:
5^{2} = 25
3^{x} = 81
3^{1} = 3
2^{0} = 1
4.4^{0} = 1
4^{\frac{5}{2}} = 32
4^{ - 2 } = 0.0625
4^{ - 3 } = \dfrac{1}{64}
x^{1.5} = 64
25^{\frac{3}{2}} = 125
4^{ - 1 } = 0.25
2^{ - 6 } = \dfrac{1}{64}
4^{2} = 16
4^{1} = 4
3^{0} = 1
\left(9.8\right)^{0} = 1
Rewrite each of the following equations in logarithmic form:
10^{2} = 100
10^{ - 2 } = \dfrac{1}{100}
10^{4} = 10\,000
10^{ - 3 } = \dfrac{1}{1000}
10^{\frac{1}{2}} = \sqrt{10}
10^{ - \frac{1}{2} } = \dfrac{1}{\sqrt{10}}
10^{-1} = 0.1
10^{-4} = 0.000\,1
Rewrite each of the following equations in logarithmic form:
x^{2.5} = 243
9^{x} = 81
Rewrite each of the following equations in exponential form:
\log_{10} 1000 = 3
\log_{10} 100\,000 = 5
\log_{10} 0.1 = - 1
\log_{10} \left(\sqrt{10}\right) = \dfrac{1}{2}
\log_{10} \left(\dfrac{1}{1000}\right) = - 3
\log_{10} \left(\dfrac{1}{\sqrt{10}}\right) = -\dfrac{1}{2}
Rewrite each of the following equations in exponential form:
\log_{4} 16 = 2
\log_{5} 5 = 1
\log_{2} 0.125 = - 3
\log_{3} \dfrac{1}{3} = - 1
\log_{5.8} 33.64 = 2
\log_{\frac{1}{3}} 9 = - 2
\log_{6} 36 = 2
\log_{2} 2 = 1
\log_{8} 1 = 0
\log_{7} \dfrac{1}{7} = - 1
\log_{8.4} 70.56 = 2
\log_{\frac{1}{3}} 81 = - 4
Rewrite each of the following equations in exponential form:
\log_{x} 64 = 2
\log_{5} x = 9
\log_{x} 32= 5
\log_{8} x = 6
For each of the following equations:
Rewrite the equation in logarithmic form.
Approximate the value of x to two decimal places.