`5^(n + 1) = 625`
`=> 5^(n + 1) = 5^4`
`=> n + 1 = 4`
`=> n = 4 -1`
`=> n = 3`
`7^n = 7^2 . 7^4`
`=> 7^n = 7^(2 + 4)`
`=> 7^n = 7^6`
`=> n = 6`
`7. 2^(3n - 1) = 224`
`=>2^(3n-1) = 224 : 7`
`=> 2^(3n-1) = 32`
`=> 2^(3n -1) = 2^5`
`=> 3n - 1 = 5`
`=> 3n = 6`
`=> n = 2`
a: =>5^(n+1)=5^4
=>n+1=4
=>n=3
b: =>7^n=7^6
=>n=6
c: =>2^(3n-1)=32
=>3n-1=5
=>3n=6
=>n=2
a) \(5^{n+1}=625\)
\(\Rightarrow5^{n+1}=5^4\)
\(\Rightarrow n+1=4\)
\(\Rightarrow n=4-1\)
\(\Rightarrow n=3\)
b) \(7^n=7^2\cdot7^4\)
\(\Rightarrow7^n=7^{2+4}\)
\(\Rightarrow7^n=7^6\)
\(\Rightarrow n=6\)
c) \(7\cdot2^{3n-1}=224\)
\(\Rightarrow2^{3n-1}=224:7\)
\(\Rightarrow2^{3n-1}=32\)
\(\Rightarrow2^{3n-1}=2^5\)
\(\Rightarrow3n-1=5\)
\(\Rightarrow3n=5+1\)
\(\Rightarrow3n=6\)
\(\Rightarrow n=\dfrac{6}{3}\)
\(\Rightarrow n=2\)