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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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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)

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