Given-that-1-log-3-x-log-27-y-express-y-in-terms-of-x-

Question Number 53675 by pieroo last updated on 24/Jan/19

Given that 1 + \log_{3} x = \log_{27} y, express y

in terms of x .

Answered by kaivan.ahmadi last updated on 24/Jan/19

\log_{3} 3 + \log_{3} x = \log_{3^{3}} y \Rightarrow \log_{3} 3 x = \frac{1}{3} \log_{3} y = \log_{3} y^{\frac{1}{3}} \Rightarrow

3 x = y^{\frac{1}{3}} \Rightarrow y = {(3 x)}^{3}

Answered by peter frank last updated on 24/Jan/19

1 = {l o g}_{27} y - {l o g}_{3} x

1 = \frac{1}{3} \log_{3} y - \log_{3} x

3 = \log_{3} y - 3 \log_{3} x

3 = \log_{3} (\frac{y}{x^{3}})

27 = \frac{y}{x^{3}}

27 x^{3} = y

\dots \dots