If log x^3- log 10x = log 10^5   find x

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log x^3- log 10x = log 10^5

We will use logarithm properties to solve for x.

We know that log a - log b = log a/b

==> log x^3 - log 10x = log x^3/10x = log x^2/10

==> log x^2/10 = log 10^5

Now we have two equal...

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log x^3- log 10x = log 10^5

We will use logarithm properties to solve for x.

We know that log a - log b = log a/b

==> log x^3 - log 10x = log x^3/10x = log x^2/10

==> log x^2/10 = log 10^5

Now we have two equal logarithm with equal bases. Then, we conclude that the logs are equal.

==> x^2 /10 = 10^5

Now let us multiply both sides by 10.

==> x^2 = 10^5 * 10

We know that x^a * x^b = x^(a+ b)

==> x^2 = 10^(5+ 1)

==> x^2 = 10^6

Now we will re-write 10^6.

We know that 10^6 = 10^(2*3) = (10^3)^2.

==> x^2 = ( 10^3) ^2

Now we will take the root of both sides.

==> x = 10^3= 1000

==> Then, the answer is x = 1000.

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