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 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=(\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`

Answer 2

Part 1)
`x=-0.07`

Part 2)
`y=2.48`

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`