Help needed with this question:
Log10(B^3) - (Log10(AB)-Log10(A/B))
Familiar with logarithmic properties?
The Four Basic Properties of Logs
1. log(xy) = log(x) + log(y)
2. log(x/y) = log(x) - log(y)
3. log(xn) = n log(x)
4. log(x) = log(x) / log(b)
$\displaystyle \log(b^3) - \log(ab) + \log(\frac{a}{b})$
$\displaystyle 3\log(b) - \log(a) - \log(b) + \log(a) - \log(b)$
$\displaystyle \log(b)$
Hello, oldskool_89!
There are number of ways to simplify this . . .
We have: .$\displaystyle \log(B^3) - \log(AB) + \log\left(\frac{A}{B}\right) \;= \;\log\left(\frac{B^3}{AB}\cdot\frac{A}{B}\right) \;=\;\log(B)$$\displaystyle \log(B^3) - \bigg[\log(AB)- \log\left(\frac{A}{B}\right)\bigg]$