Exponential functions

  • Thread starter Corkery
  • Start date
  • #1
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Homework Statement


Solve the equation:
(1/9)^m = 81^m + 4


Homework Equations


I know how to do a similar equation:
9^2p = 27^p-1

3^4p = 3^3p-1

cancel out the 3's because the base is the same.

4p = 3p-1
-3p -3p

1p = -1


The Attempt at a Solution


I know how to do ones like that but when it comes to this I start to struggle with fractions. :'(.

I'm totally lost and cant even make an attempt to this equation. I'm not asking for the answer but just a maybe the first step or something to get me on the right path.
 

Answers and Replies

  • #2
195
1
How about converting some terms to powers of 9?
 
  • #3
14
0

Homework Statement


Solve the equation:
(1/9)^m = 81^m + 4


Homework Equations


I know how to do a similar equation:
9^2p = 27^p-1

3^4p = 3^3p-1

cancel out the 3's because the base is the same.

4p = 3p-1
-3p -3p

1p = -1


The Attempt at a Solution


I know how to do ones like that but when it comes to this I start to struggle with fractions. :'(.

I'm totally lost and cant even make an attempt to this equation. I'm not asking for the answer but just a maybe the first step or something to get me on the right path.
[tex] (\frac{1}{9})^m = 81^{m+4} [/tex]

[tex] (9^{-1})^m = (9^2)^{m+4} [/tex]

[tex] (9)^{-m} = (9)^{2m+8} [/tex]

[tex] -m = 2m+8 [/tex]

[tex] -8 = 3m [/tex]

[tex] m = - \frac{8}{3} [/tex]
 
  • #4
symbolipoint
Homework Helper
Education Advisor
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Corkey,

The way you manage your notation is very important: you wrote
(1/9)^m = 81^m + 4


2. Homework Equations
I know how to do a similar equation:
9^2p = 27^p-1

3^4p = 3^3p-1

cancel out the 3's because the base is the same.

4p = 3p-1
-3p -3p

1p = -1
which showed your original equation of difficulty to be very different from what you meant. In simple text-based expressiveness, you needed proper grouping saying (1/9)^m = 81^(m+4); The way you first wrote it, the "4" was not included as part of the exponent.
 

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