Find maximum no. of roots
Algebra
Level
2
Find the number of real roots which satisfy the equation above.
0
1
4
2
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1 solution
Write the original equation as:
(1 + 1/2 + 1/4) * 2^x = (1 + 1/7 + 1/49) * 7^x;
or (1 + 1/2 + 1/4) / ( (1 + 1/7 + 1/49) = (7/2)^x;
or (7/4)/(57/49) = (7/2)^x;
or 7/4 * 49/57 = (7/2)^x;
or 343/228 = (7/2)^x;
or x = log_(7/2) {343/228}.
Hence, there is just one root x to the original equation.