We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
395
1
avatar+12 

Hi. I'm having trouble with this logarithmic equation I'm being asked to do without a calculator. The answer is 8 - the only problem I have is getting there. It's the $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{16}}}}$$ that's really messing me up. A little help?

Equation

 

Thanks, guys :)

 Jul 20, 2014

Best Answer 

 #1
avatar+99659 
+10

Let's take this by parts

log32 + log 161/2 = lg 9 + log 4  = log (9*4)  = log(36)  .... and.....

[log 12 - log 2]   =  log (12/2)  = log (6)

So, the first fraction becomes.....log(36)/log(6) = log(6)2 / log(6) = 2log(6)/log(6) = 2

And the numerator of the second fraction is.......

[2 - log 25 + 2log8] = ] 2 - log25 + log 82 ] = [2 - log25 + log64]

Notice, in terms of logs, that 2 can be written as log 100

So we have..

[log100- log25 + log 64] = [ log (100/25) + log64] = [log(4) + log (64)] =

log (4 * 64) = log(256) = log(16)2 = 2log(16)

And the denominator is....

log 3√16 = log 16 (1/3) = (1/3) log 16

And the second fraction becomes...

[2log(16)] / [(1/3)log(16)]  = 2/(1/3) = 6

So...combining the result of the first fraction and the second fraction, we have

2 + 6  = 8

And there you go.......

 

 Jul 20, 2014
 #1
avatar+99659 
+10
Best Answer

Let's take this by parts

log32 + log 161/2 = lg 9 + log 4  = log (9*4)  = log(36)  .... and.....

[log 12 - log 2]   =  log (12/2)  = log (6)

So, the first fraction becomes.....log(36)/log(6) = log(6)2 / log(6) = 2log(6)/log(6) = 2

And the numerator of the second fraction is.......

[2 - log 25 + 2log8] = ] 2 - log25 + log 82 ] = [2 - log25 + log64]

Notice, in terms of logs, that 2 can be written as log 100

So we have..

[log100- log25 + log 64] = [ log (100/25) + log64] = [log(4) + log (64)] =

log (4 * 64) = log(256) = log(16)2 = 2log(16)

And the denominator is....

log 3√16 = log 16 (1/3) = (1/3) log 16

And the second fraction becomes...

[2log(16)] / [(1/3)log(16)]  = 2/(1/3) = 6

So...combining the result of the first fraction and the second fraction, we have

2 + 6  = 8

And there you go.......

 

CPhill Jul 20, 2014

15 Online Users

avatar
avatar