Math, asked by chakri3032, 1 year ago

find x if 2log5+1/2 log9-log3=logx​

Answers

Answered by AbhijithPrakash
7

\rule{300}{1.05}

Answer:

2\log _{10}\left(5\right)+\dfrac{1}{2}\log _{10}\left(9\right)-\log _{10}\left(3\right)=\log _{10}\left(x\right)\quad :\quad x=25

Step-by-step explanation:

\rule{300}{1.05}

2\log _{10}\left(5\right)+\dfrac{1}{2}\log _{10}\left(9\right)-\log _{10}\left(3\right)=\log _{10}\left(x\right)

\rule{300}{1.05}

\mathrm{Apply\:log\:rule}:\quad \:a=\log _b\left(b^a\right)

$2\log_{10}\left(5\right)+\dfrac{1}{2}\log_{10}\left(9\right)-\log_{10}\left(3\right)=\log_{10}\left(10^{2\log_{10}\left(5\right)+\dfrac{1}{2}\log_{10}\left(9\right)-\log_{10}\left(3\right)}\right)=\log_{10}\left(25\right)$

\log _{10}\left(25\right)=\log _{10}\left(x\right)

\rule{300}{1.05}

\mathrm{When\:the\:logs\:have\:the\:same\:base:\:\:}\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)

\mathrm{For\:}\log _{10}\left(25\right)=\log _{10}\left(x\right)\mathrm{,\:\quad solve\:}25=x

25=x

\rule{300}{1.05}

\mathrm{Switch\:sides}

x=25

\rule{300}{1.05}

\mathrm{The\:solution\:is}

x=25

\rule{300}{1.05}

Attachments:
Similar questions