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log 10, 000 = y What does y equal?

 

options: 4

5

-10

3

 Dec 16, 2019
 #1
avatar+43 
0

log(10,000) = 4 = y

rewrite 10,000 in power base form. = 10000 = 10^4

apply the log rule,\( \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\)

\(\log _{10}\left(10^4\right)=4\log _{10}\left(10\right)\)

so, \(4\log _{10}\left(10\right)\)

apply the other log rule: \(\log _a\left(a\right)=1\)

\(\log _{10}\left(10\right)=1\)

= 1*4

= 4

 Dec 16, 2019
 #2
avatar+19789 
0

log10 10000 = y

From the definition of logs:

Log10  x = y         exactly if 10y    =   x

log10 10000 = y        if    10y =10000         for 10y=10000    ,    y MUST = 4

 Dec 16, 2019

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