SOLUTION: Describe how to obtain the third answer in each row from the first two questions? a) log [base 8]512, log [base 2] 512,log [base 16] 512 b) log [base 4]64, log [base 8]64, log

Question 155459: Describe how to obtain the third answer in each row from the first two questions?
a) log [base 8]512, log [base 2] 512,log [base 16] 512
b) log [base 4]64, log [base 8]64, log [base 32]64
I don't know how they got the third answer for these two sequences. Can you show the steps on how you got the third answer? This way I can understand. Thank you for all the hard work!! Also, I don't know which ISBN to put because my question isn't from a textbook. Sorry!

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
First, you recall that the definition of the logarithm of a numer is:
"The logarithm of a number is the power to which the base of the logarithm must be raised to equal the number"
a) so, by the above definition, x is the power to which 16 (the base) must be raised to equal the number (512). So you can write that out as described:
The next step is to exprees the the numbers on both sides as powers of the same base.
and so make the appropriate substitutions to get:
now since the bases (2) are equal, the exponents are equal, so...
and
so
or

Similarly:
b)
but and so...
so...
and..
then...
or

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