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hammer [34]
3 years ago
8

Which of the following is equivalent to log408 rounded to three decimal places?

Mathematics
1 answer:
il63 [147K]3 years ago
4 0

The answer is: 0.564

The explanation is shown below:

1. To solve this problem you must apply the following proccedure:

2. You have the logarithm expression:

log40(8)=x

3. First, you must apply the following property:

a^{loga(x)} =x

4. Therefore, you have:

40^{log40(8)}=40^{x} \\ 8=40^{x}

5. By applying logarithm on both sides, you have:

log(8)=log(40^{x} )

6. By applying the property log(a)^{b} =blog(a):

log(8)=xlog(40)

7. Solve for x:

x=log(8)/log(40)\\ x=0.564

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