Question

log(a/4+b/4) = 1/2(log a+log b) then find the value of a/b + b/a

Answer 1

$Given \: log \Big( \frac{a}{4} + \frac{b}{4}\Big) = \frac{1}{2} ( log \:a + log \:b )$

$\implies 2 log \Big( \frac{a+b}{4}\Big) = log \:a + log \:b$

$\implies log \Big( \frac{a+b}{4}\Big)^{2} = log \:(ab)$

$\blue {( By \: Logarithmic \: Laws : }}$

$\pink { 1. n log a = log a^{n } } \\\orange { 2. log m + log n = log (mn ) }$

$\implies \Big( \frac{a+b}{4}\Big)^{2 } = ab$

$\implies \frac{(a+b)^{2}}{4^{2}} = ab$

$\implies \frac{a^{2} + b^{2} + 2ab }{16} = ab$

$\implies a^{2} + b^{2} + 2ab = 16ab$

$\implies a^{2} + b^{2} = 16ab - 2ab$

$\implies a^{2} + b^{2} = 14ab$

/* Dividing each term by ab , we get */

$\implies \frac{a^{2}}{ab} + \frac{b^{2}}{ab} = \frac{14ab}{ab}$

$\implies \frac{a}{b} + \frac{b}{a} = 14$

Therefore.,

$\red{ Value \:of \: \frac{a}{b} + \frac{b}{a}}\green{ = 14}$

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Answer 2

Step-by-step explanation:

thereforevalue of a/b + b/a = 14