Question

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

Answer 1

Answer:

Part 1) $x=-0.07$

Part 2) $y=2.48$

Step-by-step explanation:

Part 1) we have

$15^{-9x} =6$

Solve for x

Apply log both sides

$log(15^{-9x})=log(6)$

$-x*(9log(15))=log(6)$

$x=-log(6)/(9log(15))$

$x=-0.07$

Part 2) we have

$e^{y}=12$

Apply ln both sides

$ln(e^{y})=ln(12)$

$y*ln(e)=ln(12)$

Remember that

$ln(e)=1$

$y=ln(12)$

$y=2.48$

Answer 2

Answer with explanation:

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

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