InterviewSolution
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InterviewSolution
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Find the value of x if the base is 10 :5logx – 3log x –1 = 3log x + 1 – 5log x –1(a) 1 (b) 0 (c) 100 (d) 10 |
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Answer» (c) 100 5log x – 3log x –1 = 3log x + 1 – 5log x –1 ⇒ 5log x – 3log x x 3–1 = 3log x . 3 – 5log x . 5–1 ⇒ 5log x – \(\frac{1}{3}\)3log x = 3 x 3log x - \(\frac{1}{5}\) x 5log x ⇒ \(\bigg(3+\frac{1}{3}\bigg)\)3log x = \(\bigg(5+\frac{1}{5}\bigg)\)5log x ⇒ \(\frac{10}{3}\) x 3log x = \(\frac{6}{5}\)x 5log x ⇒ \(\frac{3^{log\,x}}{5^{log\,x}}\) = \(\frac{6}{5}\) x \(\frac{3}{10}\) = \(\frac{9}{25}\) ⇒ \(\big(\frac{3}{5}\big)^{log\,x}\) = \(\big(\frac{3}{5}\big)^2\) ⇒ log10 x = 2 ⇒ x = 102 = 100 |
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