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# How do you solve 5^(x+2)-5^(x+1)= 100?

Please show me the steps, I know you have to use logarithms, yet I cant seem to figure out how.

### 3 Answers

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- BrainardLv 76 years agoFavorite Answer
Another method

5^(x+2)-5^(x+1)= 100?

5^x*5^2 - 5^x*5 = 100

5^x[5^2 - 5] = 100

5^x * 20 = 100

5^x = 5

x = 1

- Iggy RockoLv 76 years ago
5^(x+2)-5^(x+1)= 100

5^(x + 1)(5) - 5^(x + 1)(1) = 100

5^(x + 1)(5 - 1) = 100

5^(x + 1)(4) = 100

5^(x + 1) = 25

5^(x + 1) = 5^2

x + 1 = 2

x = 1

- KarlLv 66 years ago
5^(x+2) - 5^(x+1)= 100

5^(x+1)(5 - 1) = 4* 5² , divide by 4

5^(x+1) = 5²

x+ 1 = 2

x = 1

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