Answer:
You need to write log_2 80 in terms of log_2 5 , such that:
log_2 80 = log_2 (8*10)
Using the properties of logarithms, you need to convert the logarithm of product in summation of logarithms, such that:
log_2 (8*10)= log_2 8 + log_2 10
Since log_2 10 = log_2 (2*5) , yields:
log_2 (8*10)= log_2 8 + log_2 (2*5)
log_2 (8*10)= log_2 8 + log_2 2 + log_2 5
You need to write 8 as power of 2, such that:
log_2 (8*10) = log_2 (2^3) + log_2 2 + log_2 5
Using the power property of logarithms, log_a b^c = c*log_a b yields:
log_2 (8*10) = 3log_2 2 + log_2 2 + log_2 5
Since log_2 2 = 1 yields:
log_2 (8*10) = 3 + 1 + 2.3219
log_2 (8*10) = 4 + 2.3219 => log_2 (8*10) = 6.3219
Hence, evaluating the given logarithm , using the indicated properties of logarithms, yields log_2 (8*10) = 6.3219 .
Step-by-step explanation:
