1. ## Simplify logs

Help needed with this question:

Log10(B^3) - (Log10(AB)-Log10(A/B))

2. Originally Posted by oldskool_89
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)

$\displaystyle \log(b^3) - \log(ab) + \log(\frac{a}{b})$

$\displaystyle 3\log(b) - \log(a) - \log(b) + \log(a) - \log(b)$

$\displaystyle \log(b)$

3. Originally Posted by oldskool_89
Help needed with this question:

Log10(B^3) - (Log10(AB)-Log10(A/B))
log10(AB) - log10(A/B) = log10(B^3)

B^3 = AB / (A/B) = AB * B/A = AB^2/A = B^2

B^3 - B^2 = 0

B^2(B - 1) = 0

Either B = 0 or B = 1

4. Hello, oldskool_89!

There are number of ways to simplify this . . .

$\displaystyle \log(B^3) - \bigg[\log(AB)- \log\left(\frac{A}{B}\right)\bigg]$
We have: .$\displaystyle \log(B^3) - \log(AB) + \log\left(\frac{A}{B}\right) \;= \;\log\left(\frac{B^3}{AB}\cdot\frac{A}{B}\right) \;=\;\log(B)$