Condensing expressions

[rachelmaddie]

Hi. Can someone please help me with the steps for condensing this?

log5 (x^5/8-x)^1/4)

 

[tkhunny]

log5 (x^5/8-x)^1/4)

Close.

log5 ((x^5)/((8-x)^(1/4)))

User more parentheses to clarify intent.
t's a little hard to read, that way.

[math]\log_{5}\left(\dfrac{x^{5}}{(8-x)^{1/4}}\right)[/math]

 

[rachelmaddie]

Close.

log5 ((x^5)/((8-x)^(1/4)))

User more parentheses to clarify intent.
t's a little hard to read, that way.

[math]\log_{5}\left(\dfrac{x^{5}}{(8-x)^{1/4}}\right)[/math]

Is there any explanation I could include since I’m suppose to justify my answers?

 

[Deleted member 4993]

Is there any explanation I could include since I’m suppose to justify my answers?

I would have added a step in between (in addition to being careful about parentheses):

5 * log₅(x) - (1/4) * log₅(8-x)

= log₅(x⁵) - log₅[(8-x)^(1/4)]

= log₅[x⁵ / (8-x)^(1/4)]

some may prefer

= (1/4) * log₅[x²⁰ / (8-x)]

 

[rachelmaddie]

I would have added a step in between (in addition to being careful about parentheses):

5 * log₅(x) - (1/4) * log₅(8-x)

= log₅(x⁵) - log₅[(8-x)^(1/4)]

= log₅[x⁵ / (8-x)^(1/4)]

I would have added a step in between (in addition to being careful about parentheses):

5 * log₅(x) - (1/4) * log₅(8-x)

= log₅(x⁵) - log₅[(8-x)^(1/4)]

= log₅[x⁵ / (8-x)^(1/4)]

Like this??

5 * log5(x) - (1/4) * log5(8-x)

= log5(x5) - log5[(8-x)(1/4)]

= log5 ((x^5)/((8-x)^(1/4)))

 

[tkhunny]

Keep in mind that there is no definition of "condensed" or "simplified". Your goal should be clarity.