SOLUTION: Can you pls. help: Solve the equation, making the bases the same log

SOLUTION: Can you pls. help: Solve the equation, making the bases the same log_8(2)=x

Question 409902: Can you pls. help:
Solve the equation, making the bases the same
log_8(2)=x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

The fast way to do this is to ask yourself the question: "What power of 8 is 2?" Since 2 is the cube root of 8 and since the exponent for cube root is 1/3, the answer to this question is 1/3.

To solve the problem as asked we start by rewriting the equation in exponential form. In general is equivalent to . Using this pattern on your equation we get:

Now we can change 8 to :

The rule for exponents when raising a power to a power is to multiply the exponents. This gives us:

We now have two equal exponential terms whose bases are the same. This can only be true if the exponents themselves are equal, too. So:
1 = 3x
Dividing by 3 we get:
1/3 = x
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