Question

Solve the equation by finding the exact solution.
ln x − ln 6 = 16

Answer 1

three useful rules:
\[\ln(a) - \ln(b) = \ln(a/b)\]\[\ln(a) + \ln(b) = \ln(ab)\]\[\ln(a^b) = b*\ln(a)\]

Answer 2

right

Answer 3

and, if:\[c = \ln(d)\]\[d = e^c\]

Answer 4

kinda lost me their

Answer 5

notice the 1st rule listed by Euler271 ... that one will come very handy right off

Answer 6

it would become ln(x/6)=16 correct?

Answer 7

which will be x/6=e^16?

Answer 8

it's just what ln(x) is: the inverse operation of e^x.

solution:

\[\ln(x) - \ln (16 )= 16\]\[\ln \left( \frac{ x }{ 6 } \right) = 16\]\[\frac{ x }{ 6 } = e^{16}\]

Answer 9

yes :)

Answer 10

x = 6e^(16)

Answer 11

sweet! thanks so much

Answer 12

glad i could help:)

Answer 13

your the best