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1. It is seen by an unarmed eye that your writing for the equation is INCORRECT.
2. The correct writing is this
log(10^(x+2)) = 2x + 1. (1)
3. The solution is this:
log(10^(x+2)) = x + 2.
Hence, the equation (1) is equivalent to
x + 2 = 2x + 1, or
x = 1.
Answer. x = 1.
