document.write( "Question 409902: Can you pls. help:
\n" ); document.write( "Solve the equation, making the bases the same\r
\n" ); document.write( "\n" ); document.write( "log_8(2)=x \n" ); document.write( "

Algebra.Com's Answer #288399 by jsmallt9(3758) $\"\"$ $\"About$

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$\"log%288%2C+%282%29%29+=+x\"$
\n" ); document.write( "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.

\n" ); document.write( "To solve the problem as asked we start by rewriting the equation in exponential form. In general $\"log%28a%2C+%28p%29%29+=+q\"$ is equivalent to $\"p+=+a%5Eq\"$ . Using this pattern on your equation we get:
\n" ); document.write( " $\"2+=+8%5Ex\"$
\n" ); document.write( "Now we can change 8 to $\"2%5E3\"$ :
\n" ); document.write( " $\"2+=+%282%5E3%29%5Ex\"$
\n" ); document.write( "The rule for exponents when raising a power to a power is to multiply the exponents. This gives us:
\n" ); document.write( " $\"2+=+2%5E%283x%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"2%5E1+=+2%5E%283x%29\"$
\n" ); document.write( "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:
\n" ); document.write( "1 = 3x
\n" ); document.write( "Dividing by 3 we get:
\n" ); document.write( "1/3 = x \n" ); document.write( "

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