document.write( "Question 263697: 125^(x+3)=(5^(2x))/(15625) \n" ); document.write( "

Algebra.Com's Answer #194362 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
(There are errors in another solution provided.)
\n" ); document.write( " $\"125%5E%28x%2B3%29=%285%5E%282x%29%29%2F%2815625%29\"$
\n" ); document.write( "As in that other solution, the key to a relative simple solution is to recognize that 125 and 15625 are powers of 5. (I don't immediately recognize that 15625 is a power of 5 but, since it ends in 5, it could be. And we can find out which power of 5 it is, if any, by finding successive powers of 5. It turns out to be $\"5%5E6\"$ .)

\n" ); document.write( "So we can start our solution by replacing the 125 and 15625 by 5 to the appropriate power:
\n" ); document.write( " $\"%285%5E3%29%5E%28x%2B3%29=%285%5E%282x%29%29%2F%285%5E6%29\"$
\n" ); document.write( "Using our rules for exponents we get:
\n" ); document.write( " $\"5%5E%283x%2B9%29=5%5E%282x-6%29\"$
\n" ); document.write( "We have a power of 5 equal to another power of 5. The only way this can be true is if the exponents are equal:
\n" ); document.write( " $\"3x%2B9+=+2x+-+6\"$
\n" ); document.write( "Solving this we get
\n" ); document.write( " $\"x+=+-15\"$

\n" ); document.write( "(This is the same answer as the other solution. One error in the other solution is that it has $\"125%5Ex%2B125%5E3\"$ and $\"5%5E%283x%29%2B5%5E9\"$ in several places. The plus symbols should be multiplication symbols. And later the solution assumes
\n" ); document.write( " $\"5%5E%283x%29%2B5%5E9\"$
\n" ); document.write( "is equal to
\n" ); document.write( " $\"5%5E%283x%2B9%29\"$ .
\n" ); document.write( "But they are not equal. These two errors happen to cancel each other out which is why the answer accidentally works out to be correct.) \n" ); document.write( "

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