document.write( "Question 641766: Solve x in the following exponential notation $\"9%5E%282x%2B1%29=243\"$ \n" ); document.write( "

Algebra.Com's Answer #403790 by DrBeeee(684) $\"\"$ $\"About$

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Since 9 = 3^2, 9^(2x+1) is
\n" ); document.write( "(1) LS = 3^(4x+2)
\n" ); document.write( "and
\n" ); document.write( "(2) RS = 243 = 3^5
\n" ); document.write( "Equating (1) and (2) we have
\n" ); document.write( "(3) 3^(4x+2) = 3^5,
\n" ); document.write( "Since the bases are equal we can equate the exponents and obtain
\n" ); document.write( "(4) 4x + 2 = 5 or
\n" ); document.write( "(5) 4x = 3 or
\n" ); document.write( "(6) x = 3/4
\n" ); document.write( "Check your answer
\n" ); document.write( "Is (9^(2*(3/4)+1) = 243)?
\n" ); document.write( "Is (9^(10/4) = 243)?
\n" ); document.write( "Is (9^(5/2) = 243)?
\n" ); document.write( "Is ((9^(1/2))^5 = 243)?
\n" ); document.write( "Is (3^5 = 243)?
\n" ); document.write( "Is (243 = 243)? Yes
\n" ); document.write( "Answer is x = 3/4
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