Question 914023
 log(base 5) (x/2)


 log(base 6) cuberoot of x^2 + 7 


 log(base 8)(xy)^7


"sorry if it comes off confusing I just didn't know how to write those out"


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You ask about expanding each expression.


log(base 5) (x/2)
Text for algebra.com:  log(5,(x/2))
rendering tags: {{{log(5,(x/2))}}}
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{{{highlight(log(5,x)-log(5,2))}}}


 log(base 6) cuberoot of x^2 + 7 
You probably meant this:
Text for algebra.com:  log(6,(root(3,(x^2+7))))
rendering tags:  {{{log(6,(root(3,(x^2+7))))}}}
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The cubed root means "to the one-third power".
{{{highlight((1/3)log(6,(x^2+7)))}}}
No way in Real numbers to split the argument expression any further.


 log(base 8)(xy)^7
Text for algebra.com:  log(8,((xy)^7))
rendering tags:  {{{log(8,((xy)^7))}}}
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{{{7*log(8,((xy)))}}}
{{{highlight(7*log(8,x)+7*log(8,y))}}}