Question

log(a+b)/c+log c/a? when b is four times a​

Answer 1

Step-by-step explanation:

log(a+b)/c + log c/a.......(1)

given that: b=4a

so substitute b in (1)

log(5a/c)+log(c/a)

log(5ac/ac)..........ac gets cancelled

=> log 5

Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf{ log \bigg( \frac{a + b}{c} \bigg) + log \bigg( \frac{c}{a} \bigg)}$

When b is four times a

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

$\displaystyle \sf{ log \bigg( \frac{a + b}{c} \bigg) + log \bigg( \frac{c}{a} \bigg)}$

$\displaystyle \sf{ = log \bigg( \frac{a + b}{c} \times \frac{c}{a} \bigg) }$

$\displaystyle \sf{ = log \bigg( \frac{a + b}{a} \bigg) }$

$\displaystyle \sf{ = log \bigg( \frac{a + 4a}{a} \bigg) \: \: \: \: \: \: \: \: (\because \: b = 4a) }$

$\displaystyle \sf{ = log \bigg( \frac{5a}{a} \bigg)}$

$\displaystyle \sf{ = log \: 5}$

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