Question

the valie of logabc a2b2c2​

Answer 1

the value of logabc is a4b2c1

Answer 2

SOLUTION

TO EVALUATE

$\sf log_{abc}( {a}^{2} {b}^{2} {c}^{2} )$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

EVALUATION

Here the given expression is

$\sf log_{abc}( {a}^{2} {b}^{2} {c}^{2} )$

We simplify it as below

$\sf log_{abc}( {a}^{2} {b}^{2} {c}^{2} )$

$\sf = log_{abc}( {a}^{2} {b}^{2} {c}^{2} )$

$\sf = log_{abc} \bigg[{(abc)}^{2} \bigg]$

$\sf =2 log_{abc} {(abc)}^{}$

$\sf =2 \times 1$

$\sf = 2$

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