3x [(-6) +x]= 3 (-6)+3 X10
Find value of x
Answers
Step-by-step explanation:
So we will get this straight ….. We will make use of indices and quadratic equation’s factorization method to solve this particular problem!!!!
3^ [x+2] + 3^ [-x] =10
=> [3^x * 3^2] + 1/3^x = 10
=> [3^x * 9] + 1/3^x = 10
Substituting 3^x = y, we get;
=> [y * 9] + 1/y = 10
Multiplying by 'y' on b.h.s, we get;
=> [ y^2 * 9] + 1 = 10y
=> 9y^2 - 10y + 1 = 0
=> 9y^2 - 9y - y + 1 =0
=> 9y(y-1) -1(y-1) = 0
=> (y-1)(9y-1) = 0
=> Now, y-1 = 0 OR 9y-1 = 0
=> y=1 OR y=1/9
Re-substituting y = 3^x, we get;
3^x = 1 OR 3^x = 1/9
3^x = 3^0 OR 3^x = 1/3^2
3^x = 3^0 OR 3^x = 3^(-2)
x = 0 OR x = -2
Hurray!! we got the solution.
I hope this helped you tackle the question. And in case you are giving some entrance exam where in you get MCQs of this kind of questions, no need to solve the whole thing and waste your valuable time, simply substitute the given options, when LHS = RHS for a particular option, congratulations that's the solution!!
All the best for your future!! :)
Step-by-step explanation:
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