SOLUTION: Evaluate the logarithmic expression. Do not round the expression until the final answer. When necessary, round to the nearest hundredth. log[2]32 (1/5)

Question 627858: Evaluate the logarithmic expression. Do not round the expression until the final answer. When necessary, round to the nearest hundredth.
log[2]32 (1/5)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

This expression is simple to evaluate if you understand what logarithms are and if you can figure out powers of 2. A base 2 logarithm, like yours, is an exponent that you would put one a 2. This particular logarithm is the exponent you would put on a 2 to get as a result.

So what power of 2 does result in ? The answer is easier than you think because 32 happens to be a power of 2! . Substituting this into your expression we get:

Using our exponent rule for powers of a power (i.e. multiply the exponents) we get:

Now it is easy to see what power of 2 (the 2 in the base) results in a 2 (the 2 in the argument). It is 1! So:

RELATED QUESTIONS
Evalute the following logarithmic expression. Round off your answer to two decimal places (answered by jsmallt9)

Evalute the following logarithmic expression. Round off your answer to two decimal places (answered by jsmallt9)

What interest rate would be necessary to obtain $6500 in 8 years if $5000 is the... (answered by ikleyn)

Evaluate the following expression. Round your answer to two decimal places. log15 e (answered by Alan3354)

Evaluate the following expression. Round your answer to two decimal places. log[8]... (answered by Alan3354)

Consider the equation 0.5∗e^4x =13. Solve the equation by finding an expression... (answered by solver91311)

use the change-of-base theorem to find the logarithm. log(4)^9 (simplify your answer.... (answered by Alan3354)

The population of adamsville grew from 6K to 11K in 8 years. assuming uninhibited... (answered by htmentor)

Find the area between the curves. x=-3 x=2 y=4e^4x y=3e^(4x) + 1 (Do... (answered by Fombitz)