Question

Evaluate without using a calculator
ln2+2ln3 - ln 18

Answer 1

Answer is 0 using a calculator, but i cant this answer without using a calculator

Answer 2

\[\Large \ln(2)+2\cdot \ln(3)-\ln(18)=\ln(2)+\ln(3^2)-\ln(18)\]
\[\Large \ln(2\cdot 3^2)-\ln(18)=\ln(18)-\ln(18)=\]
\[\Large \ln\left(\frac{18}{18}\right)=\ln(1)\]

and we know that \[\Huge \ln(1)=0\]
:)

Answer 3

there's an equal sign on the second row in the beginning ...

Answer 4

just want to confirm
if it is lnx + lnx
u multiply x and x together?

Answer 5

yes... ln and log have same rules:
the difference is:
normal...
\[\LARGE \log_{10}(x)\]
\[\LARGE \ln_{e}(x)\]
and when you have:
\[\LARGE \ln(x)+\ln(x)=\ln(x\cdot x)=\ln(x^2)\]

Answer 6

oh ok thanks so much :)