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

1 Answer

1 vote

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 :)

User Zaki Aziz
by
7.8k points

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