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# 2ln10+log20/log121-ln11 equals -18.743, why and how?

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2ln10+log20/log121-ln11 equals -18.743, why and how?

I was given this problem for homework but whenever I enter it into my calculator I get something completely different. What am I doing wrong?

Guest Jul 10, 2015

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Thank you so much!!

Guest Jul 10, 2015
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2ln10+log20/log121-ln11 equals -18.743, why and how?

$${\mathtt{2}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{10}}\right)}{\mathtt{\,\small\textbf+\,}}{\frac{{log}_{10}\left({\mathtt{20}}\right)}{{log}_{10}\left({\mathtt{121}}\right)}}{\mathtt{\,-\,}}{ln}{\left({\mathtt{11}}\right)} = {\mathtt{2.831\: \!933\: \!610\: \!243\: \!228\: \!5}}$$

It is because division is done before addition and subtraction   Remember PEDMAS

To do it on the calc you need to put more brackets in,  then it gives you the answer that you seek :))

( 2ln10+log20 ) / ( log121-ln11 )

$${\frac{\left({\mathtt{2}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{10}}\right)}{\mathtt{\,\small\textbf+\,}}{log}_{10}\left({\mathtt{20}}\right)\right)}{\left({log}_{10}\left({\mathtt{121}}\right){\mathtt{\,-\,}}{ln}{\left({\mathtt{11}}\right)}\right)}} = -{\mathtt{18.743\: \!302\: \!368\: \!896\: \!347\: \!2}}$$

Melody  Jul 10, 2015
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