Solve and round your answer to the nearest thousandths

Question

2^2-x=5

 

Do I replace the x with a certain number? Please explain.


Thank you.

Answer 1

This is a job for logarithms. The general rule is:

 

y = b^t   --->   log_b(y) = t

 

In our problem b = 2, t = (2 - x), and y = 5.

 

We can rewrite the equation as:

 

• log_2(5) = 2 - x

 

Therefore x = 2 - log_2(5) ≈ -0.322

Answer 2

Mark has worked this out correctly but did not explain how

he got the answer to log₂(5)

 

At that point to use the calculator we need to use the change of base formula

log₂(5) = log(5)/log(2)

 

Thus to get the final answer we plug in

 

2 - log₂5 = 2 - log5/log2 = -0.322