Question

9) Se log 2 = a, log 3 = b e log 5 = c, determine:
(a)
$log \frac{3}{4 } =$
(b)
$log \: 900 =$
​

Answer 1

$\boxed{\log{xy}=\log{x}+\log{y}}$

$\boxed{\log{\frac{x}{y}}=\log{x}-\log{y}}$

$\boxed{\log{x^n}=n\log{x}}$

$\log{2}=a\\ \log{3}=b\\ \log{5}=c$

a)

$\log{\dfrac{3}{4}}=\log{3}-\log{2^2}=\log{3}-2\log{2}=\boxed{b-2a}$

b)

$\log{900}=\log{(3^2\times10^2)}=2\log{3}-2\log{10}=\boxed{2(b-1)}$