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30) Go...
[tex] log_{b}(18) = log_{b}( {3}^{2} \times 2) =[/tex]
[tex] log_{b}( {3}^{2} ) + log_{b}(2) = [/tex]
[tex]2 log_{b}(3) + log_{b}(2) = [/tex]
[tex]2(0.562) + 0.356 =[/tex]
[tex]1.124 + 0.356 = 1.480[/tex]
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31) Go...
[tex] log_{b}( \sqrt{28} ) = log_{b}( {28}^{ \frac{1}{2} } ) = [/tex]
[tex] \frac{1}{2} log_{b}(28) = \frac{1}{2} log_{b}(7 \times 4) = \\ [/tex]
[tex] \frac{1}{2} log_{b}(7 \times {2}^{2} ) = \frac{1}{2}( \: log_{b}(7) + log_{b}( {2}^{2} ) \: )= \\ [/tex]
[tex] \frac{1}{2}( \: log_{b}(7) + 2 log_{b}(2) \: ) = \\ [/tex]
[tex] \frac{1}{2} log_{b}(7) + \frac{2}{2} log_{b}(2) = \\ [/tex]
[tex] \frac{1}{2}(0.872) + 1 \times (0.356) = \\ [/tex]
[tex]0.436 + 0.356 = 0.792[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
32) Go...
[tex] log_{b}( \frac{1}{21} ) = log_{b}( {21}^{ - 1} ) = - log_{b}(21) = \\ [/tex]
[tex] - log_{b}(7 \times 3) = - ( \: log_{b}(7) + log_{b}(3) \: ) = \\ [/tex]
[tex] - (0.872 + 0.562) = - (1.434) = \\ [/tex]
[tex] - 1.434[/tex]
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33) Go...
[tex] log_{b}(3 {b}^{2} ) = log_{ b}(3 \times {b}^{2} ) = [/tex]
[tex] log_{b}(3) + log_{b}( {b}^{2} ) = log_{b}(3) + 2 log_{b}(b) = \\ [/tex]
[tex]0.562 + 2(1) = 0.562 + 2 = [/tex]
[tex]2.562[/tex]
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34) Go...
[tex] log_{b}(1) = 0[/tex]
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Done...
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