Question

((1)/(5))^x=1/25

Answer 1

take log or ln of both sides

\[\log((\frac{ 1 }{ 5 })^x) = \log(\frac{ 1 }{ 25 }) \]

use the rule:

\[\log(a^b) = b*\log(a)\]

\[xlog(\frac{ 1 }{ 5 }) = \log(\frac{ 1 }{ 25 })\]

\[x = \frac{ \log(1/5) }{ \log(1/25) }\]

Answer 2

mistake:

\[x = \frac{ \log(1/25) }{ \log(1/5) }\]

Answer 3

you can calulate x , just making complete square of 1/25. it is (1/5)^2. so , automatically x become equal to 2.

as (1/5)^x = (1/5)^2.

Answer 4

also true

Answer 5

ohhh so it would equal to 2

Answer 6

yes @summertimesadness .

Answer 7

thank you!