Question

\(\LARGE{\color{green}{\frak{Tutorial:-}}}\)

\(\Large{Logarithms}\)

Answer 1

# \(\Large{a^x=b}\) \(\rightarrow\) Exponential Form
\(\Large{log_ab=x}\) \(\rightarrow\) Logarithmic Form

When log is defined :-
\(\Large{log_ab=x}\) is defined only & only when
\(\Large{b>0}\)
\(\Large{a>0}\)
\(\Large{a \neq1}\)

Answer 2

\(\Large{\color{violet}{\text{Log Properties}}}\)
\(\Large{1.)log_a1=0}\)
\(\Large{2.)log_am+log_an=log_a(m \times n)}\)
\(\Large{3.)log_am-log_an=log_a(\frac{m}{n})}\)
\(\Large{4.)log_aa=1}\)
\(\Large{5.)Loving \space Property :-}\)
\(\Large{a^{(log_ab)=b}}\)
\(\Large{6.)log_ab^n=n\space log_ab}\)
\(\Large{7.)log_an^b=\frac{1}{n}log_ab}\)
\(\LARGE{8.)log_an^{b^n}=log_ab}\)
\(\Large{9.)log_a0=\text{Does Not Exist}}\)
\(\LARGE{10.)log_{\frac{1}{n}n=-1}}\)
\(\Large{11.)log_n\frac{1}{n}=-1}\)
\(\LARGE{12.)log_ab=\frac{1}{log_ba}=\frac{log_mb}{log_ma}}\)

Answer 3

\[\Huge{\color{gold}{\star}\color{red}{\text{Concept Of Antilog}}}\]\[\Large{If\space {\log_ab=x}}\]\[\Large{\implies antilog_ax=b}\]

Answer 4

can you please explain \[ {7.)}\quad\& \quad{8.)}\]

Answer 5

wait sir

Answer 6

I seriously appreciate your work... friend

excellent latex work .. it must be too complex for u at least....

Answer 7

\[\large{log_a n^{b^n}}\]
\[\large{b^n log_a n}\]

Answer 8

I never knew the seventh one.

Answer 9

@UnkleRhaukus