SOLUTION: solve the following using exponential functions. what is x in log8 (x) = 6

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Question 1168318: solve the following using exponential functions. what is x in log8 (x) = 6
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the basic definition of logs states:

y = logb(x) if and only if x = b^y

the converse of this applies as well.

y = b^x if and only if x = logb(y)

the first form of the general form is applied in the case of your problem.

applying the definition of y = logb(x) if and only if x = b^y, .....

let y = 6 and let b = 8.

you get 6 = log8(x) if and only if x = 8^6.

solve for x to get x = 262144.

you get 6 = log8(262144) if and only if 262144 = 8^6.

in order to confirm this is true, you will need the log base conversion formula.

when applied to this problem, that formula states that log8(x) = log(x)/log(8).

when you say log(x), the implication is that the base of the log function is 10.

that means that log(x) means log10(x).

your calculator assumes that the log function is finding the log to the base of 10.

using the conversion formula, you get log8(x) = log(x)/log(8) becomes:

log8(262144) = log(262144)/log(8) = 6

this confirms that you get 6 = log8(262144) if and only if 262144 = 8^6.

you found log8(262144) = 6 and you found that 8^6 = 262144.

therefore 6 = log8(262144) if and only if 8^6 = 262144.

Answer by MathTherapy(10557) (Show Source):
You can put this solution on YOUR website!

solve the following using exponential functions. what is x in log8 (x) = 6

------ Converting to EXPONENTIAL form
That's ALL!! A NOVEL doesn't have to be written to solve this!!