Question

Please simplify this log I really really need the answer asap

Answer 1

step 1

Simplify the interior expression in the log

so

we have

`\frac{\frac{(a^2g^7z^8)/(b^((12))d^((45)))}{\sqrt[3]{xy}z^((23))}}{(w^2p^5)/((√(r)tv^7)/(b))}`
`\frac{\frac{(a^(2)g^(7)z^(8))/(b^((12))d^((45)))}{\sqrt[3]{xy}z^((23))}}{(w^2p^5)/((√(r)tv^7)/(b))}\frac{}{}=\frac{(a^2g^7z^8)/(b^((12))d^((45)))}{\sqrt[3]{x}yz^((23))}/(w^2p^5)/((√(r)tv^7)/(b))=\frac{(a^2g^7z^8)/(b^((12))d^((45)))*(√(r)tv^7)/(b)}{\sqrt[3]{x}yz^((23))*w^2p^5}`
`\frac{(a^(2)g^(7)z^(8))/(b^((12))d^((45)))(√(r)tv^7)/(b)}{\sqrt[3]{xy}z^((23))w^2p^5}=\frac{\frac{a^2g^7z^8r^{((1)/(2))}tv^7}{b^((13)d(45))}}{\sqrt[3]{xy}z^((23))w^2p^5}=\frac{a^2g^7z^8r^{((1)/(2))}tv^7}{b^((13))d^((45))}/\sqrt[3]{xy}z^((23))w^2p^5=\frac{a^2g^7z^8r^{((1)/(2))}tv^7}{b^((13))d^((45))\sqrt[3]{xy}z^((23))w^2p^5}`
`\frac{a^2g^7z^8r^((1\/2))tv^7}{b^((13))d^((45))\sqrt[3]{xy}z^((23))w^2p^5}=\frac{a^2g^7r^((1\/2))tv^7}{b^((13))d^((45))\sqrt[3]{xy}z^((15))w^2p^5}`

we have the expression

`log(\frac{a^2g^7r^{((1)/(2))}tv^7}{b^((13))d^((45))\sqrt[3]{xy}z^((15))w^2p^5})=log(a^2g^7r^{((1)/(2))}tv^7)-log(b^((13))d^((45))\sqrt[3]{xy}z^((15))w^2p^5)`

Simplify the first term

`log(a^2g^7r^{((1)/(2))}tv^7)=loga^2+logg^7+logr^{((1)/(2))}+logt+logv^7`
`loga^2+logg^7+logr^{((1)/(2))}+logt+logv^7=2loga+7logg+(1)/(2)logr+logt+7logv`

Simplify the second term

`log(b^((13))d^((45))\sqrt[3]{xy}z^((15))w^2p^5)=logb^((13))+logd^((45))+log\sqrt[3]{xy}+logz^((15))+logw^2+logp^5`
`logb^((13))+logd^((45))+log\sqrt[3]{xy}+logz^((15))+logw^2+logp^5=13logb+45logd+(1)/(3)logxy+15logz+2logw+5logp`

Substitute in expression

`\begin{gathered} log(a^2g^7r^{((1)/(2))}tv^7)-log(b^((13))d^((45))\sqrt[3]{xy}z^((15))w^2p^5) \\ (2loga+7logg+(1)/(2)logr+logt+7logv)-(13logb+45logd+(1)/(3)logxy+15logz+2logw+5logp) \end{gathered}`