Determine x given that `9^x=(1/3)^(1-x)`
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calendarEducator since 2010
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The value of x has to be determined for which `9^x=(1/3)^(1-x)`
`9^x=(1/3)^(1-x)`
=> `(3^2)^x = 3^(x -1)`
=> `3^(2x) = 3^(x - 1)`
As the base is the same equate the exponent
=> `2x = x - 1`
=> `x = -1`
The solution of the equation `9^x=(1/3)^(1-x)` is x = -1
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calendarEducator since 2012
write1,657 answers
starTop subjects are Math, Science, and Social Sciences
To do this we need the following.
`log(a^n) = nloga`
`log(a/b) = loga-logb`
`9^x = (1/3)^(1-x)`
Get log on both sides.
`log(9^x) = log((1/3)^(1-x))`
`xlog9 = (1-x)log(1/3)`
`xlog9 = (1-x)(log1-log3)`
`xlog9 = (1-x)(0-log3)`
`xlog9 = -log3+xlog3`
`xlog3^2 = xlog3-log3`
`2xlog3 = xlog3-log3`
`xlog3 = -log3`
`x = -1`
So the answer is x = -1