Question

Using properties of logarithms find the following values if:

Could I get help with this question (PICTURE)(30POINTS)

Answer 1

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30) Go...

`log_(b)(18) = log_(b)( {3}^(2) * 2) =`

`log_(b)( {3}^(2) ) + log_(b)(2) =`

`2 log_(b)(3) + log_(b)(2) =`

`2(0.562) + 0.356 =`

`1.124 + 0.356 = 1.480`

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31) Go...

`log_(b)( √(28) ) = log_(b)( {28}^{ (1)/(2) } ) =`

`(1)/(2) log_(b)(28) = (1)/(2) log_(b)(7 * 4) = \\`

`(1)/(2) log_(b)(7 * {2}^(2) ) = (1)/(2)( \: log_(b)(7) + log_(b)( {2}^(2) ) \: )= \\`

`(1)/(2)( \: log_(b)(7) + 2 log_(b)(2) \: ) = \\`

`(1)/(2) log_(b)(7) + (2)/(2) log_(b)(2) = \\`

`(1)/(2)(0.872) + 1 * (0.356) = \\`

`0.436 + 0.356 = 0.792`

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32) Go...

`log_(b)( (1)/(21) ) = log_(b)( {21}^( - 1) ) = - log_(b)(21) = \\`

`- log_(b)(7 * 3) = - ( \: log_(b)(7) + log_(b)(3) \: ) = \\`

`- (0.872 + 0.562) = - (1.434) = \\`

`- 1.434`

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33) Go...

`log_(b)(3 {b}^(2) ) = log_( b)(3 * {b}^(2) ) =`

`log_(b)(3) + log_(b)( {b}^(2) ) = log_(b)(3) + 2 log_(b)(b) = \\`

`0.562 + 2(1) = 0.562 + 2 =`

`2.562`

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34) Go...

`log_(b)(1) = 0`

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Done...

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