Question

Expand log (216/625) ?

Answer 1

$\red{Expanded \: form \:of \: log \frac{216}{625}}$

$= log 216 - log 625$

/* By Logarithmic law: */

$\boxed { \pink { log \frac{m}{n} = log m - log n }}$

$= log 6^{3} - log 5^{4}$

$= 3 log 6 - 4 log 5$

/* By Logarithmic law: */

$\boxed { \blue { log a^{m} = m log a }}$

$= 3 log ( 2 \times 3 ) - 4 log 5$

$= 3( log 2 + log 3 ) - 4 log 5$

/* By Logarithmic law: */

$\boxed { \orange { log (mn) = log m + log n }}$

$= 3 log 2 + 3 log 3 - 4 log 5$

Therefore.,

$\red{Expanded \: form \:of \: log \frac{216}{625}}$

$\green { = 3 log 2 + 3 log 3 - 4 log 5 }$

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