Solve for x if 3 - log x = log 10x - 3

3 - log x = log 10x - 3

To solve
the logarithm function , first we will combine constant terms of the left side,and the logarithm
terms of the right side:

==> 3 + 3 = log 10x + log
x

==> 6 = log 10x + log x

From
logarithm properties, we know that:

log a + log b = log
a*b

==> 6= log 10x*x

==>
6 = log 10x^2

Now we will use the same properties to
re-write:

==> 6 = log 10 + log
x^2

But we know that log 10 =
1

==> 6 = 1 + log x^2

Subtract 1
from both sides:

==> 5 = log
x^2

We know that log a^b = b*log
a

==> 5 = 2*log x

Now we will
divide by 2:

==> 5/2 = log
x

==> log x = 5/2

Now we will
re-write using the exponent form:

==> x =
10^(5/2) = 316.23 ( approx)