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Question
If \[\frac{3^{5x} \times {81}^2 \times 6561}{3^{2x}} = 3^7\] then x =
Options
3
-3
\[\frac{1}{3}\]
\[- \frac{1}{3}\]
Solution
We have to find the value of x provided`(3^(5x )xx 81^2 xx 6561)/(3^2x) = 3^7`
So,
`(3^(5x)xx 3^(4xx2) xx 3^8)/3^(2x) = 3^7`
By using law of rational exponents we get
`3^(5x +8 +8-2x)= 3^7`
By equating exponents we get
`5x +8 +8 -2x =7`
` 3x +16 = 7`
`3x = 7-16`
`3x=-9`
`x=(-9)/3`
`x=-3`
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