Solve the logmarithic equation

-4log (a+8) = 2

a = - 8 + sqrt (10) / 10

Step-by-step explanation:

-4log (a+8) = 2

Divide each side by - 4

-4/-4log (a+8) = 2/-4

log (a+8) = - 1/2

Raise each side to the power of 10

10 ^ log (a+8) = 10^-1/2

a+8 = 1 / sqrt (10)

Subtract 8 from each side

a + 8-8 = - 8 + 1 / sqrt (10)

a = - 8 + 1/sqrt (10)

We do not like sqrt's in the denominator

a = - 8 + sqrt (10) / 10