ln(2 y)+2 ln(y)=x make y the subject of the equation

Question

i)make y the subject of the equation

 

 

ii)evaluate y when x = 1.72

Answer 1

Thomas,

 

The object of the first part of your question is to solve for y in terms of x, right?

 

You can do this quickly by combining the logarithms on the left side of the equality using logarithm properties.

 

ln (2y) + 2 ln (y) = ln (2y) + ln(y²) = ln (2y · y²) = ln (2y³)

 

Next, put this back into the equation:

 

ln (2y³) = x,

 

and rewrite in equivalent exponential form:

 

2y³ = e^x.

 

Now, finish by solving for y:

 

y³ = e^x/2

 

y = (e^x/2)^1/3 = e^(x/3)/³√2.

 

This is just one way of writing the answer. You can use what you know about algebra to put it in a different form.

 

For part ii) you can plug in x = 1.72 into the answer from i) and simplify using a calculator.

 

y = e^(1.72/3)/³√2 ≈ 1.408

 

I rounded the answer to three decimal places, since you did not specify how to state the answer.