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Do not use a calculator and determine log_4(8^2*32*256)

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steve1234 | Student, Undergraduate | Salutatorian

Posted September 3, 2013 at 5:59 PM via web

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Do not use a calculator and determine log_4(8^2*32*256)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 3, 2013 at 6:05 PM (Answer #1)

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The value of `log_4(8^2*32*256)` has to be determined.

To determine the required value use the relation `log_a a = 1` and `log_b a^x = x*log_b a` .

First, express `8^2*32*256` as a power of 4.

`8^2*32*256`

= `64*32*256`

= `2^6*2^5*2^8`

= `2^(6+5+8)`

= `2^19`

= `4^(19/2)`

`log_4 4^(19/2)`

= `(19/2)*1`

The required value of `log_4(8^2*32*256) = 9.5`

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