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0
775
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avatar+253 

Evaluate the expression.

log 12  81 + log 12  256

 

 Jul 10, 2014

Best Answer 

 #6
avatar+124676 
+10

There is a way to get an exact answer, but it's not obvious, at first......

Note that we can write 81 as 34 and we can write 256 as 44

And using a log property, we can write

log12 81 + log12 256      .....as......

log12 34 + log 12 44 =  log12(34 * 44) = log12(3*4)4 = log12 (12)4 = 4log12(12) = 4*1 = 4

And that's it.......

 

 Jul 10, 2014
 #1
avatar+118117 
+10

log 12  81 + log 12  256

$$\frac{log81}{log12}+\frac{log256}{log12}\\\\
=\frac{log81+log256}{log12}\\\\$$

$${\frac{\left({log}_{10}\left({\mathtt{81}}\right){\mathtt{\,\small\textbf+\,}}{log}_{10}\left({\mathtt{256}}\right)\right)}{{log}_{10}\left({\mathtt{12}}\right)}} = {\mathtt{3.999\: \!999\: \!999\: \!999\: \!999\: \!7}}$$

I suspect that the exact answer is 4.  So there is probably an exact way to do this.

-----------------------

I'll think about it.  

 Jul 10, 2014
 #2
avatar+253 
+5

That is correct. 

 Jul 10, 2014
 #3
avatar+118117 
0

Thank you Sally1    (I'll take your comment as a thank you )

 Jul 10, 2014
 #4
avatar+253 
0

I meant that I had the answer but I wanted to see how it was supposed to be worked out. 

 Jul 10, 2014
 #5
avatar+118117 
0

Yes , that is what I thought Sally.

That is good - It is nice to know that my answers have been checked - we can all make mistakes.

 Jul 10, 2014
 #6
avatar+124676 
+10
Best Answer

There is a way to get an exact answer, but it's not obvious, at first......

Note that we can write 81 as 34 and we can write 256 as 44

And using a log property, we can write

log12 81 + log12 256      .....as......

log12 34 + log 12 44 =  log12(34 * 44) = log12(3*4)4 = log12 (12)4 = 4log12(12) = 4*1 = 4

And that's it.......

 

CPhill Jul 10, 2014
 #7
avatar+118117 
0

Thank you Chris.  That's great.

 Jul 10, 2014

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