What is the solution of log2x + 727 = 3?

Question

anonymous · Answer

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anonymous · Answer

@phi you've always been a huge help, do you mind helping me out for this one?

phi · Answer

The question looks like it has a typo.  It looks like 
$$ \log_{2x} $$
(log to the base 2x)  which does not make sense

anonymous · Answer

That's the question that was given to me. Do you think they're just trying to confuse us? Can it be set up differently?

phi · Answer

maybe what it says is this
$$ \log_{2x+7} 27 = 3 $$

which is log to the base "2x+7"

thought that looks peculiar, we can do this: write 27  as $3^3$
$$ \log_{2x+7} 3^3 = 3 $$
use the property
$$ \log a^b = b \log a $$ to write
$$ \log_{2x+7} 3^3 = 3 \ 3 \log_{2x+7} 3 = 3
$$

phi · Answer

divide both sides by 3
you get
$$ \log_{2x+7} 3 = 1 $$
make each side the exponent of the base 2x+7.  this "undoes the log" on the left side
$$ 3 = (2x+7)^1 \ 3 = 3x+7 $$
can you find x now ?