Question

Which of the following is equivalent to log 25 125?

A. 1.951
B. 2 over 5
C. 2 over 3
D. 3 over 2

Answer 1

http://openstudy.com/study#/updates/4fb1b3fbe4b055653427c0e1

Answer 2

I think it's D but on other people and sites are saying it's c ,

i know logb^y = log y / log b ... so log 125 / log 25 = 1.5 which is 3/2 .. am i right?

Answer 3

@peterg2001

Answer 4

\[\log_a b = \frac{ \log b }{ \log a }\] change of base formula

Answer 5

yes you are right !!!

Answer 6

nope 3/2 is right people how are saying is 2/3 they are doing opposite
change of base formula is log b/log a( base)
base should be at the denominator :-(

Answer 7

:-) **

Answer 8

Thank you so much .. @Nnesha , so it's D right? , because multiple people were saying c for some reason and i just wanted to clarify that ..

Answer 9

yes it's D\[\huge\rm log_{25} 125\] this is your question right so change of base formula \[\frac{ \log 125 }{ \log 25 }\]

Answer 10

\[ \log_{25} 125 = x\]
if we raise both sides to the base 25, this "undoes" the log on the left side.
in other words, another way to write this equation is
\[ 125= 25^x \]
You might know that 5*5= 25 and 5*5*5= 125
so we can write it as
\[ 5^3 = \left( 5^2\right)^x \]
or

\[ 5^{2x}= 5^3 \]
the bases are equal (to 5), so the exponents are equal
\[ 2x= 3 \\ x= \frac{3}{2} \]
that means we have found
\[ \log_{25} 125 = \frac{3}{2} \]

Answer 11

Thank you so much @phi for your help ,