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Question
If \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\] then x =
Options
2
3
5
4
Solution
We have to find the value of x provided \[\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},\]
So,
\[\frac{3^{2x - 8}}{3^2 × 5^2} = \frac{5^3}{5^x}\]
By cross multiplication we get
`3^(2x-8) xx 5^x = 3^2xx5^2 xx5^3`
By equating exponents we get
`3^(2x-8) = 3^2`
`2x - 8 = 2`
`2x= 2+8`
`2x = 10`
`x=10/2`
`x=5`
And
`5^x = 5^(3+2)`
`x=3+2`
`x=5`
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