Question

what are the laws of logarithms

Answer 1

Since a logarithm is simply an exponent which is just being written down on the line, we expect the logarithm laws to work the same as the rules for exponents, and luckily, they do.

Exponents Logarithms
\displaystyle{b}^{m}\times{b}^{n}=b
m
×b
n
= \displaystyle{b}^{{{m}+{n}}}b
m+n
\displaystyle{{\log}_{{b}}{x}}{y}=log
b
​ xy= \displaystyle{{\log}_{{b}}{x}}+{{\log}_{{b}}{y}}log
b
​ x+log
b
​ y
\displaystyle{b}^{m}\div{b}^{n}=b
m
÷b
n
= \displaystyle{b}^{{{m}-{n}}}b
m−n
\displaystyle{{\log}_{{b}}{\left(\frac{x}{{y}}\right)}}=log
b
​ (
y
x
​ )= \displaystyle{{\log}_{{b}}{x}}-{{\log}_{{b}}{y}}log
b
​ x−log
b
​ y
\displaystyle{\left({b}^{m}\right)}^{n}={b}^{{{m}{n}}}(b
m
)
n
=b
mn
\displaystyle{{\log}_{{b}}{\left({x}^{n}\right)}}=log
b
​ (x
n
)= \displaystyle{n}{{\log}_{{b}}{x}}nlog
b
​ x
\displaystyle{b}^{1}={b}b
1
=b \displaystyle{{\log}_{{b}}{\left({b}\right)}}={1}log
b
​ (b)=1
\displaystyle{b}^{0}={1}b
0
=1 \displaystyle{{\log}_{{b}}{\left({1}\right)}}={0}log
b
​ (1)=0
Note: On our calculators, "log" (without any base) is taken to mean "log base 10". So, for example "log 7" means "log107".

Answer 2

Hope this helps you....!