Helpp?? LOGARITHMS: 1. log[5] 29=? and answer has to be rounded to nearest millionth??whats the answer?

2. log b( square root of a/ c) =?? … log b a= 10, log b c=3 .

3. log b(square root of a/c ^2) =?? …log b a=6, log b c= -3.

thank you!!

Answerer 1

log₅(29) = ln(29) / ln(5) ~ 2.09221853417

2. log_b(√(a/c) = 1/2 * log_b(a/c) = 1/2 * (log_b(a) – log_b(c))
–> plug in log_b(a) = 10 and log_b(c) = 3

1/2 * (10 – 3) = 7/2

If you meant:

log_b(√(a) / c) then it’s 1/2 * log_b(a) – log_b(c) = 1/2 * 10 – 3 = 5 – 3 = 2

3) log_b(√(a) / c²) = 1/2 * log_b(a) – 2 * log_b(c) = 3 + 6 = 9