Question

if ln5=a and ln3=b write ln0.12 as an expression in a and b

Answer 1

.12=2*3/2*5

Answer 2

0.12=12/10=6/5=2*3/5

ln(2*3/5)=ln2+ln3-ln5=ln2+b-a

Answer 3

sorry that is wrong.
\[.12=\frac{2\times 3}{(2\times 5)^2}\]

Answer 4

actually .12=12/100 but that is the right idea

Answer 5

i mean sgadi has the right method

Answer 6

so ln2+b-a is the answerÉ

Answer 7

not what i get

Answer 8

what you get im lost

Answer 9

ok lets go slow

Answer 10

\[.12=\frac{12}{100}\]

Answer 11

now reduce this to
\[\frac{12}{100}=\frac{3}{25}\]

Answer 12

now it is easy

Answer 13

ish

Answer 14

but where does a and b come in

Answer 15

\[ln(\frac{3}{25})=ln(\frac{3}{5^2})\]

Answer 16

not there yet is is coming

Answer 17

\[ln(\frac{3}{5^2})=ln(3)-ln(5^2)\]

Answer 18

=\[ln(3)-2ln(5)\]

Answer 19

ln(12/100)=ln(3/25)=ln3-ln5^2=ln3-2ln5=b-2a

Answer 20

and there is your a and b.
\[ln(3)-2ln(5)=a-2b\]

Answer 21

the gimmick was to rewrite these in terms of ln(3) and ln(5)

Answer 22

b=ln3
a=ln5
so its b-2a

Answer 23

thanks you!