document.write( "Question 93454: need to solve -
\n" ); document.write( "log9 (1/3) = y
\n" ); document.write( "Don't get - have put it in 9^y = 1/3 - now what
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\n" ); document.write( "thanks \n" ); document.write( "

Algebra.Com's Answer #68062 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
You are on the right track with:
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\n" ); document.write( " $\"9%5Ey+=+1%2F3\"$
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\n" ); document.write( "Now you can make a couple of changes. First, recognize that $\"1%2F3\"$ is equivalent to
\n" ); document.write( " $\"3%5E-1\"$ .
\n" ); document.write( "Substitute this into the equation to get:
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\n" ); document.write( " $\"9%5Ey+=+3%5E%28-1%29\"$
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\n" ); document.write( "Now notice that 9 is equal to $\"3%5E2\"$ . So replace the 9 with $\"3%5E2\"$ and you get:
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\n" ); document.write( " $\"%283%5E2%29%5Ey+=+3%5E%28-1%29\"$
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\n" ); document.write( "by the power rule of exponents you can multiply the exponent y by the exponent 2 to make the
\n" ); document.write( "left side of the equation change as indicated:
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\n" ); document.write( " $\"3%5E%282y%29+=+3%5E%28-1%29\"$
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\n" ); document.write( "Notice that the bases of the two sides are both 3. Therefore, for the sides to be equal, the
\n" ); document.write( "two exponents must also be equal. When you set the two exponents equal you get:
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\n" ); document.write( " $\"2y+=+-1\"$
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\n" ); document.write( "Solve for y by dividing both sides by 2 to get:
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\n" ); document.write( " $\"y+=+%28-1%29%2F2+=+-1%2F2\"$
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\n" ); document.write( "That's the answer for y.
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\n" ); document.write( "Check it out by substituting $\"-1%2F2\"$ for y in the original problem to get ...
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\n" ); document.write( " $\"log%289%2C%281%2F3%29%29+=+-1%2F2\"$
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\n" ); document.write( "When you convert this to exponential form you get:
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\n" ); document.write( " $\"9%5E%28-1%2F2%29+=+1%2F3\"$
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\n" ); document.write( "But a negative exponent becomes a positive exponent if you put it (along with its base) into
\n" ); document.write( "the denominator of a fraction. So $\"9%5E%28-1%2F2%29\"$ becomes $\"1%2F%289%5E%281%2F2%29%29\"$ and the
\n" ); document.write( "equation is then:
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\n" ); document.write( " $\"1%2F9%5E%281%2F2%29+=+1%2F3\"$
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\n" ); document.write( "Then recognize that the exponent $\"1%2F2\"$ tells you to take the square root of its base. So
\n" ); document.write( " $\"9%5E%281%2F2%29\"$ means to take the square root of 9 and the square root of 9 is 3.
\n" ); document.write( "So you can
\n" ); document.write( "replace $\"9%5E%281%2F2%29\"$ by 3 and the equation is finally reduced to:
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\n" ); document.write( " $\"+1%2F3+=+1%2F3\"$
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\n" ); document.write( "Since this is true, you know that $\"y+=+-1%2F2\"$ is the correct answer.
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\n" ); document.write( "Hope this helps you to understand where you could go with the problem. You had a good start
\n" ); document.write( "at it by correctly changing the logarithmic form to the exponential form. \n" ); document.write( "

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