Question

Log_c(A)=2 log_c(B)=5, solve log_c(A^5B^3)

Answer 1

We know that $\log_a(bc)=\log_a(b)+\log_a(c)$.

Using this rule,

$\log_c(A^5B^3)=\log_c(A^5)+\log_c(B^3)$.

We also know that $\log_c(a^b)=b\log_c(a)$.

Using this rule,

$\log_c(A^5)+\log_c(B^3)=5\log_c(A)+3\log_c(B)$

Now we know that $\log_c(A)=2,\log_c(B)=5$ so,

$5\cdot2+3\cdot5=10+15=\boxed{25}$.

Hope this helps :)