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Given log 3 = 0.477 and log 7 = 0.845, determine the approximate value of log (132 300) without using a calculator.

 

All I could think about is using the antilog of each, but then how can I estimate from there?

 

Thank you! :)

 Feb 21, 2020
 #1
avatar+150 
+1

https://web2.0calc.com/questions/determining-the-approx-value-of-this-logarithm 

This will help but not give you the answer. I myself don't know how to do this.

 Feb 21, 2020
 #2
avatar+109450 
+1

Note  that   1323  factors as  3^3 * 7^2

 

So   1323 * 100 =    132,300  =  3^3 * 7^2 * 100  =   3^3 * 7^2 * 10^2

 

So....we have

 

log (132300)  = 

 

log  ( 3^3  * 7^2  * 10^2)          using a log property  that  log (a * b * c)  = log a + log b + log c

 

log 3^3  +  log 7^2  +  log 10^2      and another  property says that   log a^b   = b log a

 

3log3 + 2 log 7  +  2* log 10   =          [ log 10  = 1 ]

 

3 (.477) + 2 (.845)  + 2(1)  ≈ 

 

5.121

 

 

cool cool cool

 Feb 21, 2020
edited by CPhill  Feb 21, 2020

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