Question

simplify 2log5 12-log5 8-2log5 3

Answer 1

if you have any numbers in front of the log, use this rule to make them powers inside of the log:\[a\log_b(x)=\log_b(x^a)\]then once you get rid of all the numbers in front of logs, use these rules to combine addition of logs and subtraction of logs (must be in the same base though!):\[\log_b(x)+\log_b(y)=\log_b(xy)\]\[\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)\]