Chapter 12 Test

Evaluate the given function. Round to the nearest thousandth.

1) $f\left(x\right)=e^{x-4}-10,f\left(6\right)$ 

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2) $f\left(x\right)=\ln \left(x+7\right)+4,f\left(11\right)$ 

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Simplify.

3) ${\log }_{12}144$ 

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4) $\ln e^{-3}$ 

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Rewrite as a single logarithmic expression. Simplify if possible. Assume that all variables represent positive real numbers.

5) ${\log }_{4}3136-{\log }_{4}49$ 

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6) $2{\log }_{b}x+5{\log }_{b}y-3{\log }_{b}z$ 

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Rewrite as the sum or difference of logarithmic expressions whose arguments have an exponent of 1. Simplify if possible. Assume that all variables represent positive real numbers.

7) $\ln \left(\frac{a^4{b}^6}{c^{8}d}\right)$ 

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Evaluate using the change-of-base formula. Round to the nearest thousandth.

8) ${\log }_{9}62$ 

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Solve. Round to the nearest thousandth.

9) $6^{x+4}=\frac{1}{36}$ 

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10) $4^{x-9}=76$ 

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11) $e^{x+2}-6=490$ 

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Solve. Round to the nearest thousandth.

12) ${\log }_3\left(2x-11\right)={\log }_{3}5$ 

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13) ${\log }_5\left(x+65\right)+5=8$ 

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14) ${\log }_{2}x+{\log }_2\left(x-4\right)=5$ 

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15) For the function $f\left(x\right)=e^{x+9}-17,$ find its inverse function $f^{-1}\left(x\right)$.

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16) Sonia started a bank account with an initial deposit of $4200. The bank account pays 6% interest, compounded monthly. How long will it take for the deposit to grow to $6000?

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17) A painting that was purchased for $15,000 in 1992 was valued at $25,000 in 2002. If the value of the painting keeps rising exponentially at the same rate, how much will it be worth in 2025?

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18) If researchers find a wooden chalice that contains 90% of its original carbon-14, how old is the chalice? (Carbon-14 has a half-life of 5730 years.)

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Graph. Label any intercepts and asymptotes. State the domain and range of the function.

19) $f\left(x\right)=e^{x-2}-9$ 

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20) $f\left(x\right)={\log }_3\left(x+4\right)+1$ 

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