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Mathematics 15 Online
OpenStudy (anonymous):

am I wrong?! 2(log5 x + 3 log5 y − 5 log5 z)

OpenStudy (kc_kennylau):

What did you answer? :)

OpenStudy (anonymous):

OpenStudy (anonymous):

it says I'm wrong but I thought I was right

OpenStudy (kc_kennylau):

lemme see...

OpenStudy (kc_kennylau):

(sorry it'll take more time, since *.tiff is a strange extension)

OpenStudy (anonymous):

oh its Mac sorry I used the grab application

OpenStudy (kc_kennylau):

oh that's just a careless mistake, since it's \(-\log_5z^{10}\) instead of \(+\log_5z^{10}\)

OpenStudy (kc_kennylau):

understand? :)

OpenStudy (anonymous):

wait what do you mean?

OpenStudy (kc_kennylau):

i mean that it's \(\large\log_5x^2+\log_5y^6\color{red}-\log_5z^{10}\) instead of \(\large\log_5x^2+\log_5y^6\color{red}+\log_5z^{10}\)

OpenStudy (anonymous):

I get it but it stills tells me that I'm incorrect

OpenStudy (campbell_st):

well I thing your answer may need to be expressed as a fraction \[\log_{5}(\frac{x^2y^6}{z^{10}})\]

OpenStudy (campbell_st):

or perhaps \[\log_{5}(\frac{xy^3}{z^5})^2\]

OpenStudy (kc_kennylau):

yep exactly

OpenStudy (kc_kennylau):

@campbell_st use \left( and \right) instead of ( and ):p

OpenStudy (anonymous):

since I have you both here can you help me with one more?

OpenStudy (kc_kennylau):

ofc :D

OpenStudy (anonymous):

ln 5\[\sqrt[5]{8r^{7}s}\]sqrt8r^7 s

OpenStudy (anonymous):

the middle part haha I messed up

OpenStudy (kc_kennylau):

wat?

OpenStudy (kc_kennylau):

so it's \(\Huge\sqrt[5]{8r^7s}\)?

OpenStudy (anonymous):

yes sir

OpenStudy (kc_kennylau):

and what do i have to do?

OpenStudy (anonymous):

expand it forgot to add that haha

OpenStudy (kc_kennylau):

that's the simplest form and the complex-est form what do you want lol

OpenStudy (anonymous):

I expand it but it wouldn't except it :(

OpenStudy (anonymous):

Use the Laws of Logarithms to expand the expression

OpenStudy (kc_kennylau):

you mean expand \(\Large\log\sqrt[5]{8r^2s}\)?

OpenStudy (anonymous):

no its 8r^7

OpenStudy (kc_kennylau):

so it's expand \(\Large\log\sqrt[5]{8r^7}\)?

OpenStudy (anonymous):

plus an s at the end with the square root just like how you had it before but instead of a 2 its a 7 then a s but is not an exponent

OpenStudy (kc_kennylau):

can you express that...

OpenStudy (kc_kennylau):

so it's \(\Large\log\sqrt[5]{8r^7s}\)?

OpenStudy (anonymous):

Exactly like that

OpenStudy (kc_kennylau):

note that \(\Huge\sqrt[\color{green}n]{\color{blue}x}=\color{blue}x^{\frac1{\color{green}n}}\)

OpenStudy (kc_kennylau):

so \(\large\log\sqrt[5]{8r^7s}=\log(8r^7s)^\frac15=\frac15\log(8r^7s)\)

OpenStudy (anonymous):

Nope it won't take that :(

OpenStudy (kc_kennylau):

what are your options brb

OpenStudy (anonymous):

It locked out so I have no more options but thanks for everything and your time :)

OpenStudy (kc_kennylau):

no problem :)

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