Question

solve ln(x)+ln(2x)=2

Answer 1

apply this rule
ln(x) + ln(y) = ln(y*x)

Answer 2

and combine the ln expressions

Answer 3

then make both sides exponents to the base e

as

e^(ln(x)) = x

Answer 4

write it as one natural log:
ln (2x^2) = 2

write it exponential form:
e^2 = 2x^2

divide by 2:
e^2/2 = x^2

square root both sides:
plus/minus (1/sqrt2) * e = x

Answer 5

then check... the solution... one does not work...

Answer 6

this is still confusing. Is there an easier way

Answer 7

both our solutions utilized the properties of logs:

\[\large \log_b {MN} = \log_bM + \log_bN\]
\[\large \log_b {\frac {M}{N}} = \log_bM - \log_bN\]
\[\large \log_bM^n=n*\log_bM\]

Answer 8

you'll just have to just practice and get used to using these properties..

Answer 9

well, I have to know this in an hour.