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schepotkina [342]
2 years ago
12

Evaluate and reduce:

Mathematics
1 answer:
AfilCa [17]2 years ago
6 0

Answer:

-31/8

Please mark me as brainliest

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If log2 5 = k, determine an expression for log32 5 in terms of k.
lukranit [14]

Answer:

log_3_2(5)=\frac{1}{5} k

Step-by-step explanation:

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log_b(x)=\frac{log_a(x)}{log_a(b)}

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log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)

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log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)

As you can see the only difference between (1) and (2) is the coefficient \frac{1}{5} :

So:

\frac{log(5)}{log(2)} =k\\

log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k

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