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The sum of all the solutions to the equation `2log_10x-log_10(2x-75)=2`a. 30b. 350c. 75d. 200 |
Answer» Given equation is , `2log_10x-log_10(2x-75) = 2` Here, solution should satisfy two conditions. (i) `x gt 0` and (ii) `2x-75 gt 0 => x gt 75/2` Now, we will solve the given equation, `2log_10x-log_10(2x-75) = 2` `=>log_10x^2-log_10(2x-75) = 2` `=>log_10(x^2/(2x-75)) = 2` `=>(x^2/(2x-75)) = 10^2` `=>(x^2/(2x-75)) = 100` `=> x^2-200x+7500 = 0` `=>x^2-150x-50x+7500=0` `=>(x-150)(x-50) = 0` So, `x = 150` and `x = 50` As both these values satisfying the above conditions (i) and (ii), both are the solutions. `:. ` Sum of all solutions `= 150+50 = 200` |
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