Question

Evaluate.
log10 0.1 =

Answer 1

what is 1/0.1?

Answer 2

\[\log _{10}0.1\]

Answer 3

tell me this : value of 1/0.1 ??

Answer 4

10

Answer 5

so we know 1/0.1 = 10
can we say that 1/10 = 0.1 ?

Answer 6

conversely*

Answer 7

hmmm..

Answer 8

\[\log_b(x)=y\iff b^y=x\] so your job is to solve
\[10^{y}=0.1\] for \(y\)

Answer 9

\[\log_{10}0.1 = \log_{10}10^{-1} = -1 \log_{10}10 = -1\]

Answer 10

your familiarity with exponential notation is what is needed, since logs are exponents

Answer 11

thanks you both...

Answer 12

if you recognize \(10^{-1}=0.1\) the you get the answer immediately. i
if you do not then it is going to be a problem
of course you could use a calculator

Answer 13

oh okay...you see they gave me steps but they go all away around the world and its just confusing!!!

Answer 14

here is the deal
if you want to solve
\[\log_b(x)=y\] for \(y\) then you write in equivalent exponential form as
\[b^y=x\] and then see if you know what \(y\) has to be
if so, you win

Answer 15

for example if i want to solve
\[\log_2(32)=y\] i write
\[2^y=32\] and see if i know \(y\)
since \(2^5=32\) i know \(y=5\) i.e.
\[\log_2(32)=5\]

Answer 16

okay I see it