SOLUTION: use the properties of logarithms and the values below to find the logarithm indicated. log8 12 =P log8 5 = q log8 9 = r Find log8 32/27 Please show steps. Thank you

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: use the properties of logarithms and the values below to find the logarithm indicated. log8 12 =P log8 5 = q log8 9 = r Find log8 32/27 Please show steps. Thank you      Log On


   

Question 558060: use the properties of logarithms and the values below to find the logarithm indicated.
log8 12 =P
log8 5 = q
log8 9 = r
Find log8 32/27
Please show steps. Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
log8 12 = P
Write the exponent equiv of logs
8%5Ep+=+12
Use common logs
log%28%288%5Ep%29%29+=+log%28%2812%29%29
use log equiv of exponents
p%2Alog%28%288%29%29+=+log%28%2812%29%29
Find the logs
.903P = 1.079
P = 1.079%2F.903
P = 1.195
:
log8 5 = q
8%5Eq+=+5
log%28%288%5Eq%29%29+=+log%285%29%29
q%2Alog%28%288%29%29+=+log%28%285%29%29
.903q = .699
q = .699%2F.903
q = .774
:
log8 9 = r
8%5Er+=+9
Do this the same way as the previous two problems
:
:
Find log8 32/27,
let the log = y
Write it log8 32/27 = y
8%5Ey+=+32%2F27
.903y = .0738
y = .0738%2F.903
y = .0817 is the log of 32/27 using the base 8
Check this on a calc: enter 8%5E.0817 results 1.185 which = 32/27