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 :)