Approximate value of the logarithmic expression

Question

Use the following approximations to find the approximate value of the Logarithmic expression.

Log_b 3= 0.5. log_b 8 = 0.9 log_b 5=0.7 log_b 20=1.3

1.) )log_b160

Answer 1

Since "160" is in the problem, you would want to break "160" down into pieces for which information is given. You are given logs of "3", "8", "5", and "20". Can you see that two of those multiply together to give you "160"? (8•20 = 160). So break 160 into 8•20:

log_b(160) = log_b(8•20)

Then using the log rule: log_b(m•n) = log_b(m) + log_b(n) you can say:

log_b(8•20) = log_b(8) + log_b(20) and since you are given that log_b(8) = 0.9 and that log_b(20) = 1.3 you can substitute those values in to get:

log_b(8) + log_b(20) = 0.9 + 1.3

So log_b(160) = 2.2