2 Answers

Dsollen · Answer 1 · 2023-10-09T15:58:35+0000

Answer:

n = 7

Explanation:

$\sf \log_4(64)^(n+1)=log_5(625)^(n-1)$

Change 64 to an exponent with base 4 and 625 to an exponent with base 5:

$\implies \sf \log_4(4^3)^(n+1)=log_5(5^4)^(n-1)$

Using exponent rule
(a^b)^c=a^(bc)

$\implies \sf \log_4(4)^(3(n+1))=log_5(5)^(4(n-1))$

Using log rule:
$\log_a(b^c)=c \log_a(b)$

$\implies \sf 3(n+1)\log_4(4)}=4(n-1)log_5(5)$

Using log rule:
$\sf \log_a(a)=1$

$\implies \sf 3(n+1)=4(n-1)$

$\implies \sf 3n+3=4n-4$

$\implies \sf 3+4=4n-3n$

$\implies \sf n=7$

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