Question

Evaluate schematically 3 log 2-1÷3 log 27+log 12-log 4+3 log 5

Answer 1

Answer:

3 log 2-1÷3 log 27+log 12-log 4+3 log 5

$=log2^3-\frac{1}{log27^3}+log3\times 4-log4+log5^3\\\\=3 log 2-\frac{1}{log{(3^3)^3}}+log3+log4-log4+3 log5\\\\ 3 log2 -\frac{1}{log3^9}+log3+3log5\\\\ =log2^3+9log3+log3+log5^3\\\\= log8+10log3+log(125)\\\\ =log8 +log3^{10}+log(125)\\\\=log[8\times3^{10}\times125}]\\\\=log{1000 \times3^{10}$

$=\log(1000)+\log3^{10}$

= log(1000) + 10 log 3

=log(10³)+10 log 3

=3 log (10)+10 log 3

=3 +10 log 3

=3 +10 × (0.477121)

= 3 +4.78

= 7.78

used the following properties of log

log a + log b=log (a b)

$log a - log b =log \frac{a}{b}\\\\ log a^b=b log a$

$log_{a}a=1\\\\ log_{10}10=1$

Answer 2

Answer:

hope this solution helps you