How do you use the Change of Base Formula and a calculator to evaluate ${log}_{\sqrt{5}} (8)$ $log_sqrt{5} (8)$ ?

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How do you use the Change of Base Formula and a calculator to evaluate ${log}_{\sqrt{5}} (8)$ $log_sqrt{5} (8)$ ?

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Answer 1 · 2015-07-05T12:05:33

I found: ${log}_{\sqrt{5}} (8) = \frac{ln (8)}{ln (\sqrt{5})} = 2.584$ $log_(sqrt(5))(8)=(ln(8))/(ln(sqrt(5)))=2.584$

Explanation:

Your calculator can evaluate, for example, natural logarithms, indicated as $ln$ $ln$ .
So you can change your log into this form by doing this:
${log}_{\sqrt{5}} (8) = \frac{ln (8)}{ln (\sqrt{5})} = 2.584$ $log_(sqrt(5))(8)=(ln(8))/(ln(sqrt(5)))=2.584$

Remembering the Change of Base Formula :
${log}_{a} (x) = \frac{{log}_{b} (x)}{{log}_{b} (a)}$ $log_a(x)=log_b(x)/log_b(a)$

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How do you use the Change of Base Formula and a calculator to evaluate ${log}_{\sqrt{5}} (8)$ $log_sqrt{5} (8)$ ?

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Explanation:

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How do you use the Change of Base Formula and a calculator to evaluate ${log}_{\sqrt{5}} (8)$ $log_sqrt{5} (8)$ ?