Solve for m: `(1/9)^m = 81^(m+4)`

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aishukul | Student, Grade 10 | (Level 3) Honors

Posted on

To solve this, first make both bases the same. 1/9^m is equivalent to 9^-m, and 9^2 equals 81 so the equation becomes: 

`9^-m=9^(2(m+4))`

Cancel out the bases since they're the same number. 

-m=2(m+4)

-m=2m+8

-8=3m

m=-8/3 This is the answer. You can also convert this into a decimal. 

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`(1/9)^m = 81^(m+4)`
The first step to make this easier is to  simplify the problems so that they have the same base.

We know that in order to make 1/9 a 9 we have to have a - for m because then we use the reciprocal

`(1/9)^m =9^-m`

81 can be simplified as 9^2 therefore

`9^-m = 9^(2(m+4))`

Now set the exponent equal and solve:

Distribute the 2

`-m = 2m + 8`

move like terms to the same side:

`-3m = 8`

Divide by -3 to get m alone

`m = -8/3`

`-8/3` is the answer

to check

`(1/9)^(-8/3) =350.5 `

`81^((-8/3 + 4)) = 350.5`

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