Question

07. Given that log 2 = x, log 3 = y and log 7 = z, express log 0.3 in terms of x, y, and z

Answer 1

SOLUTION

GIVEN

log 2 = x, log 3 = y and log 7 = z

TO DETERMINE

log 0.3 in terms of x, y, and z

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 it is given that

log 2 = x, log 3 = y and log 7 = z

Now

$\displaystyle \sf{ log(0.3) }$

$\displaystyle \sf{ = log \bigg( \frac{3}{10} \bigg) }$

$\displaystyle \sf{ = log(3) - log(10) }$

$\displaystyle \sf{ = log(3) - 1 }$

$\displaystyle \sf{ =y - 1}$

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