Question

Solve the question in the picture​

Answer 1

n = 7

Explanation:

simplify the logs according to their bases

Answer 2

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`