SOLUTION: Evalute the following logarithmic expression. Round off your answer to two decimal places 2log[8](11)

Question 382290: Evalute the following logarithmic expression. Round off your answer to two decimal places
2log[8](11)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

As soon as decimals are mentioned we should recognize that we will probably need our calculators. And our calculators only "know" base 10 and/or base e (aka ln) logarithms. So we need to convert this expression to one involving base 10 or base e logarithms.

Fortunately we have a base conversion formula for logarithms:

But to use this formula we cannot have a coefficient in front of the logarithm. The simplest way to get rid of the coefficient is to use a property of logarithms, , which allows us to move a coefficient into the argument as an exponent. Using this property on your expression we get:

Since this becomes:

Now we can use the base conversion formula. I will use base e. But you can use base 10 if you want. The final answer will work out the same either way!

2.3062877457581982
Rounded off to two decimal places this is 2.31.

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