Question

Can someone explain to me logarithmic functions?

Answer 1

\[e^{3x}=\frac{ 1 }{ 2 }\]

Answer 2

not sure what rule i can use to simplify that

Answer 3

here on the left hand side you have base as "e"

so take natural log i.e. ln of both sides as they cancel out

Answer 4

take the ln of both sides then divide by 3...

Answer 5

3x=ln1/2

Answer 6

ln e^x = x

Answer 7

\[e^{3x}=\frac{ 1 }{ 2 }\]\[3x=\ln(1/2)\]\[x=\frac{ -1 }{ 3 }\ln(2)\]

Answer 8

the book answer is -1/3ln2

Answer 9

whoa?

Answer 10

now put value of ln 1/2 on right side and divide it by 3

Answer 11

ln(1/2) is negative?

Answer 12

yeah it is...

Answer 13

ok, is there a rule for that??