An algebra problem by Ameya Salankar

Algebra Level 2

Find the number of solutions of the equation

( log ⁡ 10 ( 2 x + 1 ) ) + x = log ⁡ 10 6 + x log ⁡ 10 5 (\log_{10}{(2^{x} + 1)}) + x = \log_{10}6 +x \log_{10}5


The answer is 1.

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Ameya Salankar by Ameya Salankar , 23, India

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1 solution

James Wilson
Dec 27, 2017

x = 1 x=1 is the solution, and there can be no other because the RHS is constant, and the LHS is non-decreasing.

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