Question

Write the logarithmic expression as a single logarithm. log(2)+3log1

Answer 1

what is log(1) ?

Answer 2

ummm im not sure : /

Answer 3

10 to the power of what is 1 ?

Answer 4

all right another way:
remember the rules of logarithm
\[\Large \log (a)+\log(b)= \log(ab)\]
\[\Large \log (a)-\log(b)= \log \left( \frac ab \right)\]
\[\Large x\log (y)= \log \left( x^y\right)\]

Answer 5

\[\Large \log(2)+3\log1\]\[=\Large \log(2)+\log \left( 1^3 \right)\]\[=\Large \log(2)+\log \left( 1 \right)\]\[=\Large \log \left(2\times1 \right)\]\[=\LARGE \log \left(2\right)\]

Answer 6

the other way is to remember the rule: anything to the zeroth power is equal to 1
\[\Large x^0=1\]\[\Large \implies 0= \log_x(1)\]that gives us log of 1 is always 0 ... no matter what the base is.

\[\Large \therefore \log(2)+3\log(1)\]\[\Large=\log(2)+\ 3\cdot0\]\[\Large=\log(2)+0\]