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How do I solve log7 0.915?  Do not round until the final answer. Then round to four...

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monique06 | Valedictorian

Posted June 6, 2013 at 3:36 PM via web

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How do I solve log7 0.915? 

Do not round until the final answer. Then round to four decimal places as needed.

How do I solve (1/5)^x=17

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 6, 2013 at 3:46 PM (Answer #1)

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The equation `(1/5)^x=17` needs to be solved for x, using the operation of logarithmation, hence, you need to take logarithms both sides, such that:

`ln (1/5)^x = ln 17`

You need to use the following logarithmic identity, such that:

`ln (a^x) = x*ln a`

Reasoning by analogy yields:

`x*ln (1/5) = ln 17 => x*(ln 5^(-1)) =- ln 17 => -x*(ln 5) = ln 17`

`x = -(ln 17)/(ln 5) => x =- 2.8332/1.6094`

`x = -1.7604`

Hence, evaluating the solution to the equation `(1/5)^x=17,` using logarithmation, yields `x = -1.7604.`

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monique06 | Valedictorian

Posted June 6, 2013 at 3:56 PM (Reply #1)

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Thanks. What about the first question. solving log7 0.915

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