If log2 x= 5.2, what is the approximate value of x? Round your answer to the nearest hundredth.

Answer 1

Do things like this "in your head" using successive approximation....If the log₂x=5.2, then we can guess that x is just over 2⁵, which is 32.

Next, note that multiplying numbers is the same as adding their logs. Since, we are told that the log base 2 is 5.2, we can find the multiplier that corresponds to a log of 0.2: So, 2^0.2 = 1.149

Finally, multiply 32 times 1.149 to get 36.758. round to the nearest 1/100th to get 36.76

TEST this using your calculator

Answer 2

Hi Kush.

The most understandable way to deal with logarithms is to turn them back into exponentials.

Or you can use the "Change of Base" formula, but it may not have been introduced yet.

This logarithm has a base of 2, so the exponent-form will have a base of 2: 2^?

The "?" in 2^? is the power of the base, and the logarithm always equals the power. This log = 5.2, so that is the power or the "?" in 2^? So now we have 2^5.2

This you can put on your calculator: 36.75835

Using the change of base formula: These can also be computed on your calculator using the "log" or "ln" buttons

log_B(x) =

log x

------- or

log B

ln x

------

ln B

We would need to know "x" first in order to use this method, but since we have already found it, we can check to see if it is the correct answer.

So hit the "log" then type 36.75835 divided by "log" 2, and I get 5.20000001 (round off error)

which means we got the correct value since the original log is = 5.2