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Solve for the variable in the equations below. Round your answers to the nearest hundredth. Do not round any intermediate computations.

Solve for the variable in the equations below Round your answers to the nearest hundredth Do not round any intermediate computations class=

Respuesta :

calculista

Answer:

Part 1) [tex]x=-0.07[/tex]

Part 2) [tex]y=2.48[/tex]

Step-by-step explanation:

Part 1) we have

[tex]15^{-9x} =6[/tex]

Solve for x

Apply log both sides

[tex]log(15^{-9x})=log(6)[/tex]

[tex]-x*(9log(15))=log(6)[/tex]

[tex]x=-log(6)/(9log(15))[/tex]

[tex]x=-0.07[/tex]

Part 2) we have

[tex]e^{y}=12[/tex]

Apply ln both sides

[tex]ln(e^{y})=ln(12)[/tex]

[tex]y*ln(e)=ln(12)[/tex]

Remember that

[tex]ln(e)=1[/tex]

[tex]y=ln(12)[/tex]

[tex]y=2.48[/tex]

Answer with explanation:

The two equations which we have to solve for x and y and the way of finding it's solution is

   [tex]1.\rightarrow 15^{-9x}=6\\\\\text{Taking log on both sides}\\\\\rightarrow -9x \log 15=\log 6\\\\\rightarrow x \log 15^{-9}=\log 6\\\\\rightarrow x=\frac{\log 6}{\log 15^{-9}}}\\\\\rightarrow x=\log_{15^{-9}} 6\\\\2.\rightarrow e^y=12\\\\\text{Taking log on both sides}\\\\\rightarrow y \log e=\log 12\\\\\rightarrow y= \log 12[/tex]

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