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6 votes
Solve the question in the picture​

Solve the question in the picture​-example-1
User Gyasi
by
7.8k points

2 Answers

7 votes

Answer:

n = 7

Explanation:

simplify the logs according to their bases

Solve the question in the picture​-example-1
User Gnucki
by
8.1k points
2 votes

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

User Dsollen
by
8.1k points

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