Something's wrong at your end, as some of what you've typed shows up twice. You might want to type in the problems by hand so as to obtain proper formatting.
My understanding is that you want to rewrite log10(100x)
without involving logs.
First of all, you most probably meant
log 100x, which is "the log to the base 10 of 100x."
10
Note that 100x is a product, and so "log to the base 10 of 100x" is equal to
log to the base 10 of 100 + log to the base 10 of x
and this comes out to 2 + log x. Can't eliminate that "log" without knowing the value of "x".
1000log10(x) => 1000log x is actually exactly the same as 100log
10 x, and is equivalent to
log x^1000.
You could experiment as follows: Let y = 1000log(x)
Write the equation 10 10
and then raise the first 10 to the power y and the second 10 to the power 1000log x:
10^y = 10^[log x^1000]
This simplifies to 10^y = x^1000.
Ensure that you have copied down this problem as closely matching the original as possible.
