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Solve the logarithmic equation: log(2x + 5) + log 3 = log(x + 11) without using tables.

Mathematics

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Here are the solutions to your problems:

  1. Solve without using tables: The given equation is: log⁡(2x+5)+log⁡3=log⁡(x+11)\log(2x + 5) + \log 3 = \log(x + 11)

  1. Apply the logarithm property log⁡A+log⁡B=log⁡(AB)\log A + \log B = \log(AB) to the left side.

    $$
\log(3(2x + 5)) = \log(x + 11)
$$
$$
\log(6x + 15) = \log(x + 11)
$$

  2. Since the logarithms are equal, equate their arguments.

    $$
6x + 15 = x + 11
$$

  3. Step 3

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