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RoseWind [281]
4 years ago
5

The total cost of the nicest trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the check up and clea

ning and then had four cavities filled, each of which cost the same amount. Which shows the correct equation in value of X, the cost of each cavity filling?

Mathematics
1 answer:
Leni [432]4 years ago
8 0
X= 134.60, or if you want the equation, 628.35= 89.95+4x

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PLEASE HELP ASAP 25 PTS TO RIGHT/BEST ANSWER
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Subtract 1111 from both sides

5{e}^{{4}^{x}}=22-115e​4​x​​​​=22−11


 

Simplify 22-1122−11 to 1111

5{e}^{{4}^{x}}=115e​4​x​​​​=11



 

Divide both sides by 55

{e}^{{4}^{x}}=\frac{11}{5}e​4​x​​​​=​5​​11​​



 

Use Definition of Natural Logarithm: {e}^{y}=xe​y​​=x if and only if \ln{x}=ylnx=y

{4}^{x}=\ln{\frac{11}{5}}4​x​​=ln​5​​11​​



 

: {b}^{a}=xb​a​​=x if and only if log_b(x)=alog​b​​(x)=a

x=\log_{4}{\ln{\frac{11}{5}}}x=log​4​​ln​5​​11​​



 

Use Change of Base Rule: \log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}log​b​​x=​log​a​​b​​log​a​​x​​

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Use Power Rule: \log_{b}{{x}^{c}}=c\log_{b}{x}log​b​​x​c​​=clog​b​​x
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x=\frac{\log{\ln{\frac{11}{5}}}}{2\log{2}}x=​2log2​


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