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(i) We have , ` x^(-1//2) log_(0.5) x = 1` <br> `rArr log_(0.5) x = sqrtx` <br> To find the number of solutions, we must draw the graphs of `y=sqrtx and y = log_(0.5) x` and find the number of points of their intersection.<br> Graphs of functions are as shown in the following figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_TRI_C01_S01_019_S01.png" width="80%"> <br> From the figure, we see that graphs intersect at only one point. <br> Hence, there is only one solution. <br> (ii) We have ` x^(2)-4x+3-log_(2) x = 0` <br> or ` x^(2) - 4x+3 = log_(2) x` <br> Let us draw the graphs of ` y = x^(2) - 4x + 3 and y = log_(2) x`. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_TRI_C01_S01_019_S02.png" width="80%"> <br> From the figure, we see that graphs intersect at two points. <br> Hence, there are two solutions.Transcript

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00:00 - 00:59 | hello guys are today's question in find the number of solutions of the following equation is x to the power minus half into log x to the base 0.5 equals to 1 and second equation is x square - 4 x + 3 - 3 log x to the base 2 = 20 and have to find the number of solutions for this that is we have to find out how many values of extra there that satisfies the equation solution first equation to the power minus 2 log x to the base point 5 = 21 when you will simplify it you will get log x to the power 0.5 equals to root now we have to find out the number of solutions when we have to find only the number of solutions the best method is to draw |

01:00 - 01:59 | the two graphs will intersect at how many points in those points will be the number of solutions to these two graph we know that graph will be like this at the same time the graph of y equal to root x will be like this as we can see these graphs intercepted onley point to the number of solutions for this equation is given only now let's find the number of solutions for the equation is x square - 4 x + 3 - log x to the base 2 = 20 that is x square - 4 |

02:00 - 02:59 | X + 3 = 2 log x to the base to draw the graph of these equations also this is why this is exactly as this is greater than to the graph of this log increasing and the graph of this quadratic and something like this the roots of the quadratic are 13 and this point will be 032 this is the graph of y = 2 X square + 4 x square - 4 x + 3 as you can see |

03:00 - 03:59 | is graph intersect at two points to the number of solution for this equation will be used to thanks it has only a true solution hence the answer is and 2 respectively thank you |

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