# Proving the laws of logarithms Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Adapting the ideas

Can you adapt the ideas in the proof to produce convincing proofs of the following results?

$\log_c a - \log_c b = \log_c \frac{a}{b}$

$n\log_c a = \log_c a^n$

$\dfrac{1}{n}\log_c a = \log_c a^{\frac{1}{n}}$

$(\log_a b) \times (\log_b c)=\log_a c$

What conditions must $a,b,c,n$ satisfy?