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

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Question 382290: Evalute the following logarithmic expression. Round off your answer to two decimal places
2log[8](11)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Alog%288%2C+%2811%29%29
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:
log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
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, q%2Alog%28a%2C+%28p%29%29+=+log%28a%2C+%28p%5Eq%29%29, which allows us to move a coefficient into the argument as an exponent. Using this property on your expression we get:
log%288%2C+%2811%5E2%29%29
Since 11%5E2+=+121 this becomes:
log%288%2C+%28121%29%29
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!
ln%28121%29%2Fln%288%29
4.7957905455967411%2F2.0794415416798359
2.3062877457581982
Rounded off to two decimal places this is 2.31.