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avatar+37 

Solve for \(m:\left(\frac{1}{49}\right)^{4m-2} = 7^{-10m-2}.\)

 

Thanks a bunch!cool

 Sep 14, 2020
 #1
avatar+936 
+1

(1/49)^(4m - 2) = 7^(- 10m - 2)

(4m-2) Log (1/49) = (- 10m - 2 ) Log 7

(4m - 2)(- 1.6902) = (- 10m - 2)(0.8451)

- 6.7608m + 3.3804 = - 8.451m - 1.6902

- 6.7608m + 8.451m = - 1.6902 - 3.3804

1.6902m = - 5.0706

m = - 11.8314 / 1.6902

m = - 3

 

Link:https://ph.answers.yahoo.com/question/index?qid=20180123030240AASHvba

 

P.S. You use IMGflip?

 Sep 14, 2020
 #2
avatar+31093 
+5

Notice that \(\frac{1}{49}=7^{-2}\)  so we have \((7^{-2})^{4m-2}=7^{-10m-2}\)  or  \(7^{-8m+4}=7^{-10m-2}\)

 

We can equate exponents:   -8m + 4 = -10m - 2  so  2m = -6  or  m = -3

 Sep 14, 2020
 #3
avatar+37 
+1

yes, that's what I got too! nice job!cool

 Sep 14, 2020

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