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Whitepunk [10]
2 years ago
11

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

Mathematics
1 answer:
vlabodo [156]2 years ago
3 0

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 :)

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