Question

solve lnx - ln6 = 0

Answer 1

you can add ln(6) on both sides

Answer 2

assume a,b>0
ln(a)=ln(b)
implies a=b

Answer 3

wait what? lol

Answer 4

So like.. Ln6x =0 ?

Answer 5

Have you tried doing what I suggested?
Adding ln(6) on both sides?

Answer 6

and then compare the insides

Answer 7

hmm can we apply quotient rule here ?

Answer 8

also a-a=0
for what number x is ln(x) the same as ln(6)

Answer 9

you could @Nnesha

Answer 10

\[\log(\heartsuit)=\log(\spadesuit)\iff \heartsuit=\spadesuit\]

Answer 11

lnx - ln6 =lne6 ?

Answer 12

ln(x)-ln(6)=0
is the same as saying
ln(x)=ln(6)
for what number x is both sides the same

Answer 13

use what I said earlier or what satellite just said
that if ln(a)=ln(b) then a=b

Answer 14

So x=6?

Answer 15

yes!

Answer 16

ln(6)-ln(6) is totally zero

Answer 17

so x=6 definitely satisfies the equation

Answer 18

Thanks!

Answer 19

let me see if i get 6 hmm
quotient rule\[\large\rm ln y - ln x = \ln \frac{ x }{ y}\]
so \[\ln \frac{x}{6}=0\]
take e both sides
\[e^{\ln}( \frac{ x }{ 6 })= e^0\]
e an ln cancels out
e^0 =1
\[\cancel{e^{\ln}}( \frac{ x }{ 6 })= e^0\]
\[\frac{ x }{ 6 }=1 \rightarrow x=6\]

Answer 20

on that one step where you have ln(x/6)=0
you can also recall that ln(1)=0
and then solve the equation x/6=1

Answer 21

cool!