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\text { Given: } 2 \log _{10} x+1=\log _{10} 250 \text { , find: }

(i) x

\text { (ii) } \log _{10} 2 x

• Solution

• Transcript  "hello guys welcome back to little homework i'm ravan kumar working as a tutor that you do so today we are going to solve this very interesting question so first they give that to 2 log 10 2 log x base 10 plus 1 is equals to log 250 base 10 okay so now they are asking us to find first for x here from this equation first we need to be finding what is the x and then after that we should find this value okay so here 2 log x square x by x base 10 plus this one can be written as log 10 right so log 10 is equals to log 250 base 10 right so this is the thing here now after that it can be written as log x square plus log 10 is equals to log 250 base 10 so now again it can be written as log a plus log base equals to log of a plus base log of x square into log a plus log b is equals to log a into b so that is x square into 10 so that is equals to log of 250 base 10 here so this log and this log will be getting cancel and 10 x square is equals to 250 so this 0 and 0 will be getting cancel and x square is equals to 25 so x is equals to plus or minus 5 so that is only the answer here so let's we should take the x as 10 5 plus 5 okay so x is equals to plus 5 here now after that just substitute the x value here that is log 2 into 5 base 10 so that is equals to log 10 base 10 so the answer will be 1 so answer here is 1 so i hope you understood what i've done if you have any doubts please comment below don't forget to subscribe to this channel thank you so much for watching then stay tuned thank you"

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