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How do you find the value of #log_2 8# using the change of base formula?

Answer 1

Sadie Ackerman

The change of base formula states:

#color(green)(log_n(a) = loga/logn)#

So:

#log_2(8)#

#=> log8/log2#

Write in powers of #2#.

#=>(log2^3)/(log2^1)#

Use the rule #logn^a = alogn#.

#=>(3log2)/(1log2)#

#=> 3#

Hopefully this helps!

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Answer 2

Sadie Ackerman

To find the value of ( \log_2 8 ) using the change of base formula, we can use the formula:

[ \log_b a = \frac{\log_c a}{\log_c b} ]

where ( a ) is the number whose logarithm is being taken, ( b ) is the base of the logarithm we want to find, and ( c ) is the base of the logarithm we can easily calculate.

In this case, we want to find ( \log_2 8 ). We can rewrite this logarithm using a base we can easily calculate, such as base 10:

[ \log_2 8 = \frac{\log_{10} 8}{\log_{10} 2} ]

Now, we can calculate the logarithms:

[ \log_{10} 8 = \log_{10} 2^3 = 3 \log_{10} 2 ]

Therefore:

[ \log_2 8 = \frac{3 \log_{10} 2}{\log_{10} 2} = 3 ]

So, ( \log_2 8 = 3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.