SOLUTION: Evaluate log8 64. I worked it out to log8=log8 64/64=log 64-log8 64. Is this right?

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Question 185449This question is from textbook saxon algebra 2
: Evaluate log8 64.
I worked it out to log8=log8 64/64=log 64-log8 64.
Is this right? This question is from textbook saxon algebra 2

Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!

log8 64
.
Basically, the problem is asking what value of 'x' is this true?
8^x = 64
.
Of course, we know that:
8^2 = 64
.
Therefore, x = 2
.
So:
log8 64 = 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given expression.


... Set "y" equal to the expression


... Rewrite the equation using the property:

You can probably see that the answer is 2 (since 8 squared is 64), but let's keep going...


... Rewrite 8 as 2%5E3


... Rewrite 64 as 2%5E6


... Multiply the exponents.


Since the bases are both equal to 2, this means that the exponents are equal.


... Set the exponents equal to one another.


... Divide both sides by 3.


... Reduce



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Answer:


So the solution is


However, remember that we let (in the second step), to this means that