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Rewrite the following problems using exponent rules. Then, solve using logarithms.

1. 3(0.99)4t = 15
2. 4(1.01)3 + t = 8

Rewrite the following problems using exponent rules. Then, solve using logarithms-example-1
User Eldi
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Answer:

1. 3(0.96059601^t) = 15; t = -40.03

2. 4.121204(1.01^t) = 8; t = 66.66

Explanation:

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

(a^b)(a^c) = a^(b+c)

The solution for an exponential problem using logarithms is ...

a·b^x = c ⇒ log(c/a)/log(b) = x

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1. Rewrite: (3)(0.99^4)^t = 15 ⇒ 3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

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2. Rewrite: 4(1.01^3)(1.01^t) = 8 ⇒ 4.121204(1.01^t) = 8

Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66

User Vikram Eklare
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