Question

log[2](27) is the first term of a geometric sequence
common ration is log[2](y)
what are the ranges of the values of y to make a possible sum of series to infinity?

what is the exact value of y if the infinity sum of series is 3?

by sum of series to infinity i mean
a/1-r
just incase i worded it wrong and you didn't know what i meant.

Answer 1

y > 2

Answer 2

Solve for y
\[ \log_2 27 \left ( \frac{1}{1 - \log_2y}\right ) = 3 \]

Answer 3

better done this way
\[ 1 = \log_2 2\]
\[ 1 - \log_2y = \log_2(2/y)\]
\[ \frac{\log_227}{\log_2(2/y)} = \log_{2/y} 27\]
Now it seems lot easy to solve!!

Answer 4

do not understand
it seems you missed a step or two