# How do you evaluate log_15 (1/225)?

Oct 4, 2016

${\log}_{15} \left(\frac{1}{225}\right) = - 2$

#### Explanation:

${\log}_{2} 8 = 3$ is another way of writing ${2}^{3} = 8$
That is the easy one to remember!!
So ${\log}_{15} \left(\frac{1}{225}\right) = x$ is the same thing as ${15}^{x} = \left(\frac{1}{225}\right)$

${15}^{x} = \left(\frac{1}{15} ^ 2\right)$
${15}^{x} = {15}^{-} 2$
So $x = - 2$