Question

Choose the correct option.
The correct value of logs 125 base 5- log16 base 2
is:​

Answer 1

$\red{ The \: value \: of \: log_{5} \:125 - log_{2} \:16} \\= log_{5} \:5^{3} - log_{2} \:2^{4}\\= 3 log_{5}\:5 - 4 log_{2}\: 2$

/* By Logarithmic law */

$\boxed{\pink{ log_{a}\: x^{m} = m log_{a}\: x}}$

$= 3\times 1 - 4 \times 1$

$\boxed{ \blue{\because log_{a}\: a = 1 }}$

$= 3 - 4 \\= -1$

Therefore.,

$\red{ The \: value \: of \: log_{5} \:125 - log_{2} \:16} \\\green { = -1 }$

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