How to solve logarithmic problem: log k(k/a^3)= log k a= 10, log k b = -0.4, log k c

[Jan1232]

How to solve following: log k(k/a^3)=

log k a= 10, log k b = -0.4, log k c = 16

 

[Dr.Peterson]

How to solve following: log k(k/a^3)=

log k a= 10, log k b = -0.4, log k c = 16

This needs clarification, because you didn't use subscripts. I think you mean this:

Find log_k(k/a³), given that log_k a = 10.
​

(We don't need to know anything about b and c, which are not in this expression.)

One approach is to rewrite log_k a = 10 in exponential form, to show what a is in terms of k; then put that into the log expression and simplify.

Another approach is to expand log_k(k/a³), to express it in terms of the log of a, and then put in the given value.

Can you do one or the other of those? Please show whatever work you can do, so we can see where you need help.