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Using the change of base formula how do I find the value of  log 8   0.848...

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monique06 | (Level 3) Valedictorian

Posted June 4, 2013 at 7:03 PM via web

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Using the change of base formula how do I find the value of  log 8   0.848 (logarithm)?

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

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 4, 2013 at 7:21 PM (Answer #1)

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Evaluate `log_8 0.848` :

If you can't remember the change of base formula, here is an approach to use. Let `log_8 0.848=x` .

Now rewrite in exponential form:

`8^x=0.848`

Take a logarithm of both sides. Which one? It really doesn't matter, except many scientific calculators only calculate log base 10 and log base e (the natural logarithm) so choose one of these.

`ln8^x=ln(0.848)` Use the power property of logs:

`xln8=ln(0.848)` Now divide:

`x=(ln(0.848))/(ln8)`

This, by the way, is the change of base formula. `log_b c=(lnc)/(lnb)=(logc)/(logb)=(log_k c)/(log_k b)` for any choice of natural number k>1.

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`x=(ln0.848)/(ln8)~~-0.0793`

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Check: `8^(-0.0793)~~0.84797874` or 0.848

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted June 5, 2013 at 12:16 AM (Answer #2)

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You can apply this property of logarithm: `log_ba = loga/(logb).`

So, in your problem `log_8(0.848)`

a = 0.848 and b = 8. Applying the property, you have:

`log_8(0.848) = log(0.848)/(log8)`

Thus, the answer is -0.07928794337.

Rounding that off to four decimal places gives you -0.0793. 

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