# How do you write the equation log_(1/5) (25)=-2 in exponential form?

Oct 8, 2016

${\log}_{\frac{1}{5}} 25 = - 2 \text{ " hArr " } {\left(\frac{1}{5}\right)}^{-} 2 = 25$

#### Explanation:

Recall: $\text{ "log_a b = c " "hArr " } {a}^{c} = b$

The two forms are interchangeable and give the same information, just with a different subject.

Remember: "The base stays the base and the other two swop around"

${\log}_{10} 100 = 2 \text{ }$ asks the question:

"What power of 10 will give 100?" Or

"What index will make 10 into 100?" The answer is 2.

${10}^{2} = 100 \text{ }$ states that 10 raised to the power of 2 will give the answer 100.

${\log}_{\frac{1}{5}} 25 = - 2 \text{ " hArr " } {\left(\frac{1}{5}\right)}^{-} 2 = 25$

Let's check:

${\left(\frac{1}{5}\right)}^{-} 2 = {\left(\frac{5}{1}\right)}^{2} = 25$