Question

(log 18- log 3) / log 9 in detail ??​

Answer 1

Question

(log 18- log 3) / log 9 in detail ??

Answer

$\sf\frac{ log(18) - log(3) }{ log(9) }$

${\boxed{\sf{\blue{We \: know \: that \: log(a) - log(b) = log( \frac{a}{b} ) }}}}$

=

$\sf \frac{log(6) }{log(9)}$

=

$\sf \frac{log(6) }{log( {3}^{2} )}$

=

$\sf \frac{log(2 \times 3) }{2log(3)}$

=

$\sf \frac{log2 + log(3) }{2log(3)}$

We know that log 2 = 0.3010, log3 = 0.477

=

$\sf \frac{0.3010 + 0.477 }{2 \times 0.477}$

= 0.815

Other formulae used :-

• Log(ab) = log a + log b
• log a^m = m log a