Question

use properties of logarithms to expand the logarithmic expression as much as possible. where possible, evaluate logarithmic expressions without using a calculator.
log (1,000,000x) = \square

Explanation:

Step1: Apply Product Rule of Logarithms

The product rule of logarithms states that $\log(ab) = \log(a) + \log(b)$. For the expression $\log(1000000x)$, we can apply this rule by letting $a = 1000000$ and $b = x$. So we get $\log(1000000) + \log(x)$.

Step2: Evaluate $\log(1000000)$

We know that $1000000 = 10^6$. By the definition of a logarithm, if we assume the base of the logarithm is 10 (common logarithm), then $\log_{10}(10^6) = 6$ because $\log_b(b^n)=n$.

Answer:

$6 + \log(x)$