MHB Finding the Value of $\log_{10}\left({5*\sqrt[3]{14}}\right)$

[cbarker1]

I need some help finding the value of this $\log_{10}\left({5*\sqrt[3]{14}}\right)$

With
$$\log_{10}\left({2}\right)=.30$$ $$\log_{10}\left({3}\right)=.48$$ and $\log_{10}\left({7}\right)=.85$ is given in the textbook.

First I use
$\log_{10}\left({5}\right)+\log_{10}\left({\sqrt[3]{14}}\right)$
I use
$\log_{10}\left({5}\right)+\frac{1}{3}*[\log_{10}\left({2}\right)+\log_{10}\left({7}\right)]$
I need to how to find out the $\log_{10}\left({5}\right)$ and I know how to use the values above into the expression.

Thank
Cbarker

 

[mathmari]

I need some help finding the value of this $\log_{10}\left({5*\sqrt[3]{14}}\right)$

With
$$\log_{10}\left({2}\right)=.30$$ $$\log_{10}\left({3}\right)=.48$$ and $\log_{10}\left({7}\right)=.85$ is given in the textbook.

First I use
$\log_{10}\left({5}\right)+\log_{10}\left({\sqrt[3]{14}}\right)$
I use
$\log_{10}\left({5}\right)+\frac{1}{3}*[\log_{10}\left({2}\right)+\log_{10}\left({7}\right)]$
I need to how to find out the $\log_{10}\left({5}\right)$ and I know how to use the values above into the expression.

Thank
Cbarker

$\log_{10}\left({5}\right)=\log_{10}\left({\frac{10}{2}}\right)=\log_{10}\left({10}\right)-\log_{10}\left({2}\right)=1-\log_{10}\left({2}\right)$

 

[MarkFL]

I need some help finding the value of this $\log_{10}\left({5*\sqrt[3]{14}}\right)$

With
$$\log_{10}\left({2}\right)=.30$$ $$\log_{10}\left({3}\right)=.48$$ and $\log_{10}\left({7}\right)=.85$ is given in the textbook.

First I use
$\log_{10}\left({5}\right)+\log_{10}\left({\sqrt[3]{14}}\right)$
I use
$\log_{10}\left({5}\right)+\frac{1}{3}*[\log_{10}\left({2}\right)+\log_{10}\left({7}\right)]$
I need to how to find out the $\log_{10}\left({5}\right)$ and I know how to use the values above into the expression.

Thank
Cbarker

I just wanted to make the comment that your post could be used as a model for effectively getting help. You clearly stated the problem and what you did and where you are stuck. Well done! (Yes)