Question

express a single logarithm: log c 10+log c 4

Answer 1

logs add to multiplication:

logc(10) + logc(4) = logc(10*4) = logc(40)

Answer 2

The logarithm of a product is the sum of the logarithms of the factors, hence
\[\log_b(xy) = \log_b (x) + \log_b (y). \]
So
\[\log_c (10) + \log_c (4)=\log_c(4*10) = \log_c(40)\]

Answer 3

The logarithm of a product is the sum of the logarithms of the factors, hence
\[\log_b(xy) = \log_b (x) + \log_b (y). \]
So
\[\log_c (10) + \log_c (4)=\log_c(4*10) = \log_c(40)\]