Question

log864 – log644096 is

Answer 1

We know that log base 8 of 64 = 2

                        log base 64 of 4096 = 2


So 2 - 2 = 0

Hope this helps!

Answer 2

SOLUTION

TO DETERMINE

$\displaystyle \sf{ log_{8}(64) - log_{64}(4096) }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\sf log_{a}( {b}^{m} ) = m log_{a}(b)$

$\displaystyle \sf{ log_{a}(a) = 1 }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ log_{8}(64) - log_{64}(4096) }$

We simplify it as below

$\displaystyle \sf{ log_{8}(64) - log_{64}(4096) }$

$\displaystyle \sf{ = log_{8}( {8}^{2} ) - log_{64}( {64}^{2} ) }$

$\displaystyle \sf{ =2 log_{8}( {8}^{} ) - 2log_{64}( {64}^{} ) }$

$\displaystyle \sf{ =2 - 2 }$

$\displaystyle \sf{ = 0 }$

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